Pub Date : 2023-07-06DOI: 10.1007/s10203-023-00405-1
M. Baumann
{"title":"Correction to: Beating the market? A mathematical puzzle for market efficiency","authors":"M. Baumann","doi":"10.1007/s10203-023-00405-1","DOIUrl":"https://doi.org/10.1007/s10203-023-00405-1","url":null,"abstract":"","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"40 1","pages":"731 - 733"},"PeriodicalIF":1.1,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73657593","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 : 2023-06-07DOI: 10.1007/s10203-023-00403-3
G. Giorgi, B. Jiménez, V. Novo
{"title":"Dini and Hadamard directional derivatives in multiobjective optimization: an overview of some results","authors":"G. Giorgi, B. Jiménez, V. Novo","doi":"10.1007/s10203-023-00403-3","DOIUrl":"https://doi.org/10.1007/s10203-023-00403-3","url":null,"abstract":"","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"60 5 Pt 2 1","pages":"355 - 377"},"PeriodicalIF":1.1,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88628684","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 : 2023-05-30DOI: 10.1007/s10203-023-00402-4
Leonie Violetta Brinker, Hanspeter Schmidli
Abstract We consider a Cramér–Lundberg model representing the surplus of an insurance company under a general reinsurance control process. We aim to minimise the expected time during which the surplus is bounded away from its own running maximum by at least $$d>0$$ d>0 (discounted at a preference rate $$delta >0$$ δ>0 ) by choosing a reinsurance strategy. By analysing the drawdown process (i.e. the absolute distance of the controlled surplus model to its maximum) directly, we prove that the value function fulfils the corresponding Hamilton–Jacobi–Bellman equation and show how one can calculate the value function and the optimal strategy. If the initial drawdown is critically large, the problem corresponds to the maximisation of the Laplace transform of a passage time. We show that a constant retention level is optimal. If the drawdown is smaller than d , the problem can be expressed as an element of a set of Gerber–Shiu optimisation problems. We show how these problems can be solved and that the optimal strategy is of feedback form. We illustrate the theory by examples of the cases of light and heavy tailed claims.
摘要考虑一般再保险控制过程下保险公司盈余的cram r - lundberg模型。我们的目标是使盈余偏离其自身运行最大值的预期时间至少缩短$$d>0$$ d ＆gt;0(以优惠率贴现$$delta >0$$ δ ＆gt;0)通过选择再保险策略。通过直接分析收缩过程(即控制盈余模型到其最大值的绝对距离)，我们证明了价值函数满足相应的Hamilton-Jacobi-Bellman方程，并展示了如何计算价值函数和最优策略。如果初始衰减非常大，则问题对应于一段时间的拉普拉斯变换的最大化。我们表明，恒定的留存水平是最理想的。如果收缩小于d，则问题可以表示为一组Gerber-Shiu优化问题的一个元素。我们展示了如何解决这些问题，以及最优策略是反馈形式。我们通过轻尾索赔和重尾索赔的案例来说明这一理论。
{"title":"Optimisation of drawdowns by generalised reinsurance in the classical risk model","authors":"Leonie Violetta Brinker, Hanspeter Schmidli","doi":"10.1007/s10203-023-00402-4","DOIUrl":"https://doi.org/10.1007/s10203-023-00402-4","url":null,"abstract":"Abstract We consider a Cramér–Lundberg model representing the surplus of an insurance company under a general reinsurance control process. We aim to minimise the expected time during which the surplus is bounded away from its own running maximum by at least $$d>0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> (discounted at a preference rate $$delta >0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>δ</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> ) by choosing a reinsurance strategy. By analysing the drawdown process (i.e. the absolute distance of the controlled surplus model to its maximum) directly, we prove that the value function fulfils the corresponding Hamilton–Jacobi–Bellman equation and show how one can calculate the value function and the optimal strategy. If the initial drawdown is critically large, the problem corresponds to the maximisation of the Laplace transform of a passage time. We show that a constant retention level is optimal. If the drawdown is smaller than d , the problem can be expressed as an element of a set of Gerber–Shiu optimisation problems. We show how these problems can be solved and that the optimal strategy is of feedback form. We illustrate the theory by examples of the cases of light and heavy tailed claims.","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135690894","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 : 2023-05-25DOI: 10.1007/s10203-023-00401-5
Lars Palapies
{"title":"Laplace transforms of stochastic integrals and the pricing of Bermudan swaptions","authors":"Lars Palapies","doi":"10.1007/s10203-023-00401-5","DOIUrl":"https://doi.org/10.1007/s10203-023-00401-5","url":null,"abstract":"","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"19 1","pages":"1 - 46"},"PeriodicalIF":1.1,"publicationDate":"2023-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85882657","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 : 2023-05-24DOI: 10.1007/s10203-023-00399-w
An Chen, Steven Vanduffel
Abstract Actuarial fairness pertains to the situation in which the price of an insurance contract is equal to its expected outcome. We show that actuarial fairness leads to “unfairness” in that annuitants with higher survival rates can choose a better payoff in the sense of second-order stochastic dominance than those with lower survival rates. To deal with this issue, we propose equal utility pricing, i.e., we determine prices such that all contracts have the same (nonlinear) utility from the viewpoint of a third party (e.g., a social planner). This approach is of particular relevance with respect to the design of group self-annuitization schemes.
{"title":"On the unfairness of actuarial fair annuities","authors":"An Chen, Steven Vanduffel","doi":"10.1007/s10203-023-00399-w","DOIUrl":"https://doi.org/10.1007/s10203-023-00399-w","url":null,"abstract":"Abstract Actuarial fairness pertains to the situation in which the price of an insurance contract is equal to its expected outcome. We show that actuarial fairness leads to “unfairness” in that annuitants with higher survival rates can choose a better payoff in the sense of second-order stochastic dominance than those with lower survival rates. To deal with this issue, we propose equal utility pricing, i.e., we determine prices such that all contracts have the same (nonlinear) utility from the viewpoint of a third party (e.g., a social planner). This approach is of particular relevance with respect to the design of group self-annuitization schemes.","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135085551","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 : 2023-05-12DOI: 10.1007/s10203-023-00397-y
Nikolai Dokuchaev
The paper studies asset pricing for stochastic discrete time stock market models. The possibility of statistical evaluation of the market completeness is investigated. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper investigates if market incompleteness is robust. It is found that market incompleteness is a non-robust property as well. This is demonstrated for a basic single stock stochastic market model. This implies that, for any incomplete market from a wide class of discrete time models, there exists a complete market model with arbitrarily close stock prices. This means that incomplete markets are indistinguishable from the complete markets in the terms of market statistics.
{"title":"On statistical indistinguishability of complete and incomplete discrete time market models","authors":"Nikolai Dokuchaev","doi":"10.1007/s10203-023-00397-y","DOIUrl":"https://doi.org/10.1007/s10203-023-00397-y","url":null,"abstract":"The paper studies asset pricing for stochastic discrete time stock market models. The possibility of statistical evaluation of the market completeness is investigated. It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into a incomplete one. The paper investigates if market incompleteness is robust. It is found that market incompleteness is a non-robust property as well. This is demonstrated for a basic single stock stochastic market model. This implies that, for any incomplete market from a wide class of discrete time models, there exists a complete market model with arbitrarily close stock prices. This means that incomplete markets are indistinguishable from the complete markets in the terms of market statistics.","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135288148","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 : 2023-05-11DOI: 10.1007/s10203-023-00395-0
Udo Broll, Peter Welzel, K. Wong
{"title":"Hedging and the regret theory of the firm","authors":"Udo Broll, Peter Welzel, K. Wong","doi":"10.1007/s10203-023-00395-0","DOIUrl":"https://doi.org/10.1007/s10203-023-00395-0","url":null,"abstract":"","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"12 1","pages":"1-15"},"PeriodicalIF":1.1,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87663960","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 : 2023-05-10DOI: 10.1007/s10203-023-00396-z
F. Mehrdoust, Idin Noorani
{"title":"Implied higher order moments in the Heston model: a case study of S &P500 index","authors":"F. Mehrdoust, Idin Noorani","doi":"10.1007/s10203-023-00396-z","DOIUrl":"https://doi.org/10.1007/s10203-023-00396-z","url":null,"abstract":"","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"1 1","pages":"1-28"},"PeriodicalIF":1.1,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77831348","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 : 2023-05-08DOI: 10.1007/s10203-023-00398-x
M. Torrente
{"title":"Optimal proportional and excess-of-loss reinsurance for multiple classes of insurance business","authors":"M. Torrente","doi":"10.1007/s10203-023-00398-x","DOIUrl":"https://doi.org/10.1007/s10203-023-00398-x","url":null,"abstract":"","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"26 1","pages":"1-23"},"PeriodicalIF":1.1,"publicationDate":"2023-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88360519","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":"Correction: Revisiting the 1/N-strategy: a neural network framework for optimal strategies","authors":"Marcos Escobar-Anel, Lorenz Theilacker, Rudi Zagst","doi":"10.1007/s10203-023-00394-1","DOIUrl":"https://doi.org/10.1007/s10203-023-00394-1","url":null,"abstract":"","PeriodicalId":43711,"journal":{"name":"Decisions in Economics and Finance","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135613487","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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