Bernardo Freitas Paulo da Costa, Silvana M. Pesenti, Rodrigo S. Targino
Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework that uses only simulations of returns for estimating risk budgeting portfolios. Besides a general cutting planes algorithm for determining the weights of risk budgeting portfolios for arbitrary coherent distortion risk measures, we provide a specialised version for the Expected Shortfall, and a tailored Stochastic Gradient Descent (SGD) algorithm, also for the Expected Shortfall. We compare our algorithm to standard convex optimisation solvers and illustrate different risk budgeting portfolios, constructed using an especially designed Julia package, on real financial data and compare it to classical portfolio strategies.
{"title":"Risk budgeting portfolios from simulations","authors":"Bernardo Freitas Paulo da Costa, Silvana M. Pesenti, Rodrigo S. Targino","doi":"10.2139/ssrn.4038514","DOIUrl":"https://doi.org/10.2139/ssrn.4038514","url":null,"abstract":"Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework that uses only simulations of returns for estimating risk budgeting portfolios. Besides a general cutting planes algorithm for determining the weights of risk budgeting portfolios for arbitrary coherent distortion risk measures, we provide a specialised version for the Expected Shortfall, and a tailored Stochastic Gradient Descent (SGD) algorithm, also for the Expected Shortfall. We compare our algorithm to standard convex optimisation solvers and illustrate different risk budgeting portfolios, constructed using an especially designed Julia package, on real financial data and compare it to classical portfolio strategies.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"30 1","pages":"1040-1056"},"PeriodicalIF":0.0,"publicationDate":"2023-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76893702","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
K. Wassmuth, C. Köhler, Niels A. H. Agatz, M. Fleischmann
Given the continuing e-commerce boom, the design of efficient and effective home delivery services is increasingly relevant. From a logistics perspective, attended home delivery, which requires the customer to be present when the purchased goods are delivered, is particularly challenging. To facilitate the delivery, the service provider and the customer typically agree on a specific time window for service. In designing the service offering, service providers face complex trade-offs between customer preferences and profitable service execution. In this paper, we map these trade-offs to different planning levels and demand management levers, and structure and synthesize corresponding literature according to different demand management decisions. Finally, we highlight research gaps and future research directions and discuss the linkage of the different planning levels.
{"title":"Demand management for attended home delivery - A literature review","authors":"K. Wassmuth, C. Köhler, Niels A. H. Agatz, M. Fleischmann","doi":"10.2139/ssrn.4055952","DOIUrl":"https://doi.org/10.2139/ssrn.4055952","url":null,"abstract":"Given the continuing e-commerce boom, the design of efficient and effective home delivery services is increasingly relevant. From a logistics perspective, attended home delivery, which requires the customer to be present when the purchased goods are delivered, is particularly challenging. To facilitate the delivery, the service provider and the customer typically agree on a specific time window for service. In designing the service offering, service providers face complex trade-offs between customer preferences and profitable service execution. In this paper, we map these trade-offs to different planning levels and demand management levers, and structure and synthesize corresponding literature according to different demand management decisions. Finally, we highlight research gaps and future research directions and discuss the linkage of the different planning levels.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"56 1","pages":"801-815"},"PeriodicalIF":0.0,"publicationDate":"2023-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76761612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A choice-based optimization approach for contracting in supply chains","authors":"Nils Roemer, G. Voigt, Sven Müller","doi":"10.2139/ssrn.3986160","DOIUrl":"https://doi.org/10.2139/ssrn.3986160","url":null,"abstract":"","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"17 1","pages":"271-286"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82732531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"How to preempt attacks in multi-front conflict with limited resources","authors":"Kai A. Konrad, Florian Morath","doi":"10.2139/ssrn.4144603","DOIUrl":"https://doi.org/10.2139/ssrn.4144603","url":null,"abstract":"","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"24 1","pages":"493-500"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83300390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-22DOI: 10.48550/arXiv.2211.12150
V. Torra
Non-additive measures, also known as fuzzy measures, capacities, and monotonic games, are increasingly used in different fields. Applications have been built within computer science and artificial intelligence related to e.g. decision making, image processing, machine learning for both classification, and regression. Tools for measure identification have been built. In short, as non-additive measures are more general than additive ones (i.e., than probabilities), they have better modeling capabilities allowing to model situations and problems that cannot be modeled by the latter. See e.g. the application of non-additive measures and the Choquet integral to model both Ellsberg paradox and Allais paradox. Because of that, there is an increasing need to analyze non-additive measures. The need for distances and similarities to compare them is no exception. Some work has been done for defining $f$-divergence for them. In this work we tackle the problem of defining the optimal transport problem for non-additive measures. Distances for pairs of probability distributions based on the optimal transport are extremely used in practical applications, and they are being studied extensively for their mathematical properties. We consider that it is necessary to provide appropriate definitions with a similar flavour, and that generalize the standard ones, for non-additive measures. We provide definitions based on the M"obius transform, but also based on the $(max, +)$-transform that we consider that has some advantages. We will discuss in this paper the problems that arise to define the transport problem for non-additive measures, and discuss ways to solve them. In this paper we provide the definitions of the optimal transport problem, and prove some properties.
{"title":"The transport problem for non-additive measures","authors":"V. Torra","doi":"10.48550/arXiv.2211.12150","DOIUrl":"https://doi.org/10.48550/arXiv.2211.12150","url":null,"abstract":"Non-additive measures, also known as fuzzy measures, capacities, and monotonic games, are increasingly used in different fields. Applications have been built within computer science and artificial intelligence related to e.g. decision making, image processing, machine learning for both classification, and regression. Tools for measure identification have been built. In short, as non-additive measures are more general than additive ones (i.e., than probabilities), they have better modeling capabilities allowing to model situations and problems that cannot be modeled by the latter. See e.g. the application of non-additive measures and the Choquet integral to model both Ellsberg paradox and Allais paradox. Because of that, there is an increasing need to analyze non-additive measures. The need for distances and similarities to compare them is no exception. Some work has been done for defining $f$-divergence for them. In this work we tackle the problem of defining the optimal transport problem for non-additive measures. Distances for pairs of probability distributions based on the optimal transport are extremely used in practical applications, and they are being studied extensively for their mathematical properties. We consider that it is necessary to provide appropriate definitions with a similar flavour, and that generalize the standard ones, for non-additive measures. We provide definitions based on the M\"obius transform, but also based on the $(max, +)$-transform that we consider that has some advantages. We will discuss in this paper the problems that arise to define the transport problem for non-additive measures, and discuss ways to solve them. In this paper we provide the definitions of the optimal transport problem, and prove some properties.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"48 1","pages":"679-689"},"PeriodicalIF":0.0,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80574225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-16DOI: 10.48550/arXiv.2211.09665
Jorik Jooken, Pieter Leyman, P. D. Causmaecker
Decades of research on the 0-1 knapsack problem led to very efficient algorithms that are able to quickly solve large problem instances to optimality. This prompted researchers to also investigate whether relatively small problem instances exist that are hard for existing solvers and investigate which features characterize their hardness. Previously the authors proposed a new class of hard 0-1 knapsack problem instances and demonstrated that the properties of so-called inclusionwise maximal solutions (IMSs) can be important hardness indicators for this class. In the current paper, we formulate several new computationally challenging problems related to the IMSs of arbitrary 0-1 knapsack problem instances. Based on generalizations of previous work and new structural results about IMSs, we formulate polynomial and pseudopolynomial time algorithms for solving these problems. From this we derive a set of 14 computationally expensive features, which we calculate for two large datasets on a supercomputer in approximately 540 CPU-hours. We show that the proposed features contain important information related to the empirical hardness of a problem instance that was missing in earlier features from the literature by training machine learning models that can accurately predict the empirical hardness of a wide variety of 0-1 knapsack problem instances. Using the instance space analysis methodology, we also show that hard 0-1 knapsack problem instances are clustered together around a relatively dense region of the instance space and several features behave differently in the easy and hard parts of the instance space.
{"title":"Features for the 0-1 knapsack problem based on inclusionwise maximal solutions","authors":"Jorik Jooken, Pieter Leyman, P. D. Causmaecker","doi":"10.48550/arXiv.2211.09665","DOIUrl":"https://doi.org/10.48550/arXiv.2211.09665","url":null,"abstract":"Decades of research on the 0-1 knapsack problem led to very efficient algorithms that are able to quickly solve large problem instances to optimality. This prompted researchers to also investigate whether relatively small problem instances exist that are hard for existing solvers and investigate which features characterize their hardness. Previously the authors proposed a new class of hard 0-1 knapsack problem instances and demonstrated that the properties of so-called inclusionwise maximal solutions (IMSs) can be important hardness indicators for this class. In the current paper, we formulate several new computationally challenging problems related to the IMSs of arbitrary 0-1 knapsack problem instances. Based on generalizations of previous work and new structural results about IMSs, we formulate polynomial and pseudopolynomial time algorithms for solving these problems. From this we derive a set of 14 computationally expensive features, which we calculate for two large datasets on a supercomputer in approximately 540 CPU-hours. We show that the proposed features contain important information related to the empirical hardness of a problem instance that was missing in earlier features from the literature by training machine learning models that can accurately predict the empirical hardness of a wide variety of 0-1 knapsack problem instances. Using the instance space analysis methodology, we also show that hard 0-1 knapsack problem instances are clustered together around a relatively dense region of the instance space and several features behave differently in the easy and hard parts of the instance space.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"18 1","pages":"36-55"},"PeriodicalIF":0.0,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82513630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quantity and price risks determine key uncertainties market participants face in electricity markets with increased volatility, for instance due to high shares of renewables. In the time from day-ahead until real-time, there lies a large variation in best available information, such as between forecasts and realizations of uncertain parameters like renewable feed-in and electricity prices. This uncertainty reflects on both the market outcomes and the quantity of renewable generation, making the determination of sound trading strategies across different market segments a complex task. The scope of the paper is to optimize day-ahead and intraday trading decisions jointly for a portfolio with controllable and volatile renewable generation under consideration of risk. We include a reserve market, a day-ahead market and an intraday market in stochastic modeling and develop a multi-stage stochastic Mixed Integer Linear Program. We assess the profitability as well as the risk exposure, quantified by the conditional value at risk metric, of trading strategies following different risk preferences. We conclude that a risk-neutral trader mainly relies on the opportunity of higher expected profits in intraday trading, whereas risk can be hedged effectively by trading on the day-ahead. Finally, we show that reserve market participation implies various rationales, including the relation of expected reserve prices among each other, the relation of expected reserve prices to spot market prices, as well as the relation of the spot market prices among each other.
{"title":"Stochastic optimization of trading strategies in sequential electricity markets","authors":"Emil Kraft, M. Russo, D. Keles, V. Bertsch","doi":"10.5445/IR/1000134346","DOIUrl":"https://doi.org/10.5445/IR/1000134346","url":null,"abstract":"Quantity and price risks determine key uncertainties market participants face in electricity markets with increased volatility, for instance due to high shares of renewables. In the time from day-ahead until real-time, there lies a large variation in best available information, such as between forecasts and realizations of uncertain parameters like renewable feed-in and electricity prices. This uncertainty reflects on both the market outcomes and the quantity of renewable generation, making the determination of sound trading strategies across different market segments a complex task. The scope of the paper is to optimize day-ahead and intraday trading decisions jointly for a portfolio with controllable and volatile renewable generation under consideration of risk. We include a reserve market, a day-ahead market and an intraday market in stochastic modeling and develop a multi-stage stochastic Mixed Integer Linear Program. We assess the profitability as well as the risk exposure, quantified by the conditional value at risk metric, of trading strategies following different risk preferences. We conclude that a risk-neutral trader mainly relies on the opportunity of higher expected profits in intraday trading, whereas risk can be hedged effectively by trading on the day-ahead. Finally, we show that reserve market participation implies various rationales, including the relation of expected reserve prices among each other, the relation of expected reserve prices to spot market prices, as well as the relation of the spot market prices among each other.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"17 1","pages":"400-421"},"PeriodicalIF":0.0,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82111485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study the implications of extending the balanced cost reduction property from queueing problems to general games. As a direct translation of the balanced cost reduction property, the axiom of balanced externalities for solutions of games, requires that the payoff of any player is equal to the total externality she inflicts on the other players with her presence. We show that this axiom and efficiency together characterize the Shapley value for 2-additive games. However, extending this axiom in a straightfoward way to general games is incompatible with efficiency. Keeping as close as possible to the idea behind balanced externalities, we weaken this axiom by requiring that every player’s payoff is the same fraction of its total externality inflicted on the other players. This weakening, which we call weak balanced externalities , turns out to be compatible with efficiency. More specifically, the unique efficient solution that satisfies this weaker property is the proportional allocation of nonseparable contribution (PANSC) value, which allocates the total worth proportional to the separable costs of the players. We also provide characterizations of the PANSC value using a reduced game consistency axiom.
{"title":"Balanced externalities and the proportional allocation of nonseparable contributions","authors":"R. Brink, Y. Chun, Yukihiko Funaki, Zhengxing Zou","doi":"10.2139/ssrn.3807467","DOIUrl":"https://doi.org/10.2139/ssrn.3807467","url":null,"abstract":"In this paper, we study the implications of extending the balanced cost reduction property from queueing problems to general games. As a direct translation of the balanced cost reduction property, the axiom of balanced externalities for solutions of games, requires that the payoff of any player is equal to the total externality she inflicts on the other players with her presence. We show that this axiom and efficiency together characterize the Shapley value for 2-additive games. However, extending this axiom in a straightfoward way to general games is incompatible with efficiency. Keeping as close as possible to the idea behind balanced externalities, we weaken this axiom by requiring that every player’s payoff is the same fraction of its total externality inflicted on the other players. This weakening, which we call weak balanced externalities , turns out to be compatible with efficiency. More specifically, the unique efficient solution that satisfies this weaker property is the proportional allocation of nonseparable contribution (PANSC) value, which allocates the total worth proportional to the separable costs of the players. We also provide characterizations of the PANSC value using a reduced game consistency axiom.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"7 1","pages":"975-983"},"PeriodicalIF":0.0,"publicationDate":"2022-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87797422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-09-06DOI: 10.48550/arXiv.2209.02845
M. Dacorogna, Nehla Debbabi, M. Kratz
Cyber security and resilience are major challenges in our modern economies; this is why they are top priorities on the agenda of governments, security and defense forces, management of companies and organizations. Hence, the need of a deep understanding of cyber risks to improve resilience. We propose here an analysis of the database of the cyber complaints filed at the {it Gendarmerie Nationale}. We perform this analysis with a new algorithm developed for non-negative asymmetric heavy-tailed data, which could become a handy tool in applied fields. This method gives a good estimation of the full distribution including the tail. Our study confirms the finiteness of the loss expectation, necessary condition for insurability. Finally, we draw the consequences of this model for risk management, compare its results to other standard EVT models, and lay the ground for a classification of attacks based on the fatness of the tail.
{"title":"Building up Cyber Resilience by Better Grasping Cyber Risk Via a New Algorithm for Modelling Heavy-Tailed Data","authors":"M. Dacorogna, Nehla Debbabi, M. Kratz","doi":"10.48550/arXiv.2209.02845","DOIUrl":"https://doi.org/10.48550/arXiv.2209.02845","url":null,"abstract":"Cyber security and resilience are major challenges in our modern economies; this is why they are top priorities on the agenda of governments, security and defense forces, management of companies and organizations. Hence, the need of a deep understanding of cyber risks to improve resilience. We propose here an analysis of the database of the cyber complaints filed at the {it Gendarmerie Nationale}. We perform this analysis with a new algorithm developed for non-negative asymmetric heavy-tailed data, which could become a handy tool in applied fields. This method gives a good estimation of the full distribution including the tail. Our study confirms the finiteness of the loss expectation, necessary condition for insurability. Finally, we draw the consequences of this model for risk management, compare its results to other standard EVT models, and lay the ground for a classification of attacks based on the fatness of the tail.","PeriodicalId":11868,"journal":{"name":"Eur. J. Oper. Res.","volume":"1 1","pages":"708-729"},"PeriodicalIF":0.0,"publicationDate":"2022-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90664755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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