Pub Date : 2022-04-30DOI: 10.1080/17442508.2022.2068955
Obayda Assaad, Charles-Philippe Diez, C. Tudor
We discuss several properties of the generalized Hermite process, which is a non-Gaussian self-similar processes with self-similarity index belonging to the whole interval . We also define Wiener integral with respect to this process and as an application, we define and study its associated Ornstein–Uhlenbeck process.
{"title":"Generalized Wiener–Hermite integrals and rough non-Gaussian Ornstein–Uhlenbeck process","authors":"Obayda Assaad, Charles-Philippe Diez, C. Tudor","doi":"10.1080/17442508.2022.2068955","DOIUrl":"https://doi.org/10.1080/17442508.2022.2068955","url":null,"abstract":"We discuss several properties of the generalized Hermite process, which is a non-Gaussian self-similar processes with self-similarity index belonging to the whole interval . We also define Wiener integral with respect to this process and as an application, we define and study its associated Ornstein–Uhlenbeck process.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"1 1","pages":"191 - 210"},"PeriodicalIF":1.7,"publicationDate":"2022-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76688833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1080/17442508.2022.2056415
Quancheng Yang, Dan Wu, X. Shu
In this paper, we study the existence and some stability results of mild solutions for random impulsive stochastic partial differential equations with noncompact semigroups in Hilbert spaces. Initially, we prove the existence of mild solutions by using Hausdorff measures of noncompactness and the Mönch fixed point theorem. Then, we explore the stability with continuous dependence of initial conditions, Hyers–Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, an example is given to illustrate the abstract results obtained in this paper.
{"title":"Existence and stability results of mild solutions for random impulsive stochastic partial differential equations with noncompact semigroups","authors":"Quancheng Yang, Dan Wu, X. Shu","doi":"10.1080/17442508.2022.2056415","DOIUrl":"https://doi.org/10.1080/17442508.2022.2056415","url":null,"abstract":"In this paper, we study the existence and some stability results of mild solutions for random impulsive stochastic partial differential equations with noncompact semigroups in Hilbert spaces. Initially, we prove the existence of mild solutions by using Hausdorff measures of noncompactness and the Mönch fixed point theorem. Then, we explore the stability with continuous dependence of initial conditions, Hyers–Ulam stability and mean-square stability of the system by developing some new analysis techniques and establishing an improved inequality. Finally, an example is given to illustrate the abstract results obtained in this paper.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"31 5","pages":"168 - 190"},"PeriodicalIF":1.7,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72593009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1080/17442508.2022.2055966
E. Lépinette, Jun Zhao
In this article, we revisit the discrete-time problem of pricing a contingent claim with respect to a dynamic risk measure defined by its acceptance sets. Without any no-arbitrage condition, we show that it is possible to characterize the prices of a European claim. Our analysis reveals a natural weak no-arbitrage condition that we study. This is a condition formulated in terms of the (risk) hedging prices instead of the attainable claims. Our approach is not based on a robust representation of the risk measure and we do not suppose the existence of a risk-neutral probability measure.
{"title":"Risk-hedging a European option with a convex risk measure and without no-arbitrage condition","authors":"E. Lépinette, Jun Zhao","doi":"10.1080/17442508.2022.2055966","DOIUrl":"https://doi.org/10.1080/17442508.2022.2055966","url":null,"abstract":"In this article, we revisit the discrete-time problem of pricing a contingent claim with respect to a dynamic risk measure defined by its acceptance sets. Without any no-arbitrage condition, we show that it is possible to characterize the prices of a European claim. Our analysis reveals a natural weak no-arbitrage condition that we study. This is a condition formulated in terms of the (risk) hedging prices instead of the attainable claims. Our approach is not based on a robust representation of the risk measure and we do not suppose the existence of a risk-neutral probability measure.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"19 1","pages":"118 - 155"},"PeriodicalIF":1.7,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85665489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-29DOI: 10.1080/17442508.2022.2055967
L. Dhaouadi
In this paper, we shall give the complete solution of the equations governing the bilateral birth and death process on the path set in which the birth and death rates and where 0
本文在出生率和死亡率为0
{"title":"Bilateral birth and death process in q-calculus","authors":"L. Dhaouadi","doi":"10.1080/17442508.2022.2055967","DOIUrl":"https://doi.org/10.1080/17442508.2022.2055967","url":null,"abstract":"In this paper, we shall give the complete solution of the equations governing the bilateral birth and death process on the path set in which the birth and death rates and where 0<q<1 and . The mathematical methods employed here are based on q-Bessel Fourier analysis.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"39 1","pages":"157 - 167"},"PeriodicalIF":1.7,"publicationDate":"2022-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80118523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-15DOI: 10.1007/s00780-022-00474-x
A. Bensoussan, Guiyuan Ma, Chi Chung Siu, S. Yam
{"title":"Dynamic mean–variance problem with frictions","authors":"A. Bensoussan, Guiyuan Ma, Chi Chung Siu, S. Yam","doi":"10.1007/s00780-022-00474-x","DOIUrl":"https://doi.org/10.1007/s00780-022-00474-x","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"26 1","pages":"267 - 300"},"PeriodicalIF":1.7,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47725895","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-21DOI: 10.1007/s00780-023-00508-y
Felix Dammann, Giorgio Ferrari
{"title":"Optimal execution with multiplicative price impact and incomplete information on the return","authors":"Felix Dammann, Giorgio Ferrari","doi":"10.1007/s00780-023-00508-y","DOIUrl":"https://doi.org/10.1007/s00780-023-00508-y","url":null,"abstract":"","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"27 1","pages":"713 - 768"},"PeriodicalIF":1.7,"publicationDate":"2022-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42382780","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-16DOI: 10.1080/17442508.2022.2124871
F. Fidaleo, E. Vincenzi
It is known that the subspace generated by the eigenvectors pertaining to the peripheral spectrum of any stochastic matrix is canonically equipped with a structure of a (finite-dimensional abelian) -algebra under a canonical new product introduced by E.G. Effros and M.-D. Choi. We prove that the restriction of the action of such a stochastic matrix to this subspace is indeed a -automorphism. The following new decoherence result is then established: any Markov chain encodes a conservative -dynamical system, after isolation of the persistent part from the transient one. This result gives a partial answer to the general and currently unsolved decoherence problem for a relevant class of systems.
{"title":"Decoherence for Markov chains","authors":"F. Fidaleo, E. Vincenzi","doi":"10.1080/17442508.2022.2124871","DOIUrl":"https://doi.org/10.1080/17442508.2022.2124871","url":null,"abstract":"It is known that the subspace generated by the eigenvectors pertaining to the peripheral spectrum of any stochastic matrix is canonically equipped with a structure of a (finite-dimensional abelian) -algebra under a canonical new product introduced by E.G. Effros and M.-D. Choi. We prove that the restriction of the action of such a stochastic matrix to this subspace is indeed a -automorphism. The following new decoherence result is then established: any Markov chain encodes a conservative -dynamical system, after isolation of the persistent part from the transient one. This result gives a partial answer to the general and currently unsolved decoherence problem for a relevant class of systems.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"38 1","pages":"867 - 877"},"PeriodicalIF":1.7,"publicationDate":"2022-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79203536","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-10DOI: 10.1080/17442508.2022.2034820
Le Duc Nhien, Nguyen Huu Du, Le Huy Tien, Nguyen Trong Hieu
This paper is concerned with the tempered exponential dichotomy for random differential systems in Banach spaces. Based on the presentation of bounded solutions for a tempered exponential dichotomous system, we give a bound under which the tempered exponentially dichotomous property of perturbed systems is preserved. Some applications of our results to stochastic partial differential equations are considered.
{"title":"Tempered exponential dichotomies for linear random evolution equations","authors":"Le Duc Nhien, Nguyen Huu Du, Le Huy Tien, Nguyen Trong Hieu","doi":"10.1080/17442508.2022.2034820","DOIUrl":"https://doi.org/10.1080/17442508.2022.2034820","url":null,"abstract":"This paper is concerned with the tempered exponential dichotomy for random differential systems in Banach spaces. Based on the presentation of bounded solutions for a tempered exponential dichotomous system, we give a bound under which the tempered exponentially dichotomous property of perturbed systems is preserved. Some applications of our results to stochastic partial differential equations are considered.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"48 1","pages":"1 - 22"},"PeriodicalIF":1.7,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86417479","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-08DOI: 10.1080/17442508.2022.2041641
P. Pasricha, Dharmaraja Selvamuthu, Selvaraju Natarajan
The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a significant role in allocating capital for solvency purposes. In this article, we derive a closed-form expression for the default probability of a single firm and probability of the total number of defaults by time $t$ in a homogeneous portfolio. We use a contagion process to model the arrival of credit events causing the default and develop a framework that allows firms to have resistance against default unlike the standard intensity-based models. We assume the point process driving the credit events is composed of a systematic and an idiosyncratic component, whose intensities are independently specified by a mean-reverting affine jump-diffusion process with self-exciting jumps. The proposed framework is competent of capturing the feedback effect. We further demonstrate how the proposed framework can be used to price synthetic collateralized debt obligation (CDO). Finally, we present the sensitivity analysis to demonstrate the effect of different parameters governing the contagion effect on the spread of tranches and the expected loss of the CDO.
{"title":"A contagion process with self-exciting jumps in credit risk applications","authors":"P. Pasricha, Dharmaraja Selvamuthu, Selvaraju Natarajan","doi":"10.1080/17442508.2022.2041641","DOIUrl":"https://doi.org/10.1080/17442508.2022.2041641","url":null,"abstract":"The modeling of the probability of joint default or total number of defaults among the firms is one of the crucial problems to mitigate the credit risk since the default correlations significantly affect the portfolio loss distribution and hence play a significant role in allocating capital for solvency purposes. In this article, we derive a closed-form expression for the default probability of a single firm and probability of the total number of defaults by time $t$ in a homogeneous portfolio. We use a contagion process to model the arrival of credit events causing the default and develop a framework that allows firms to have resistance against default unlike the standard intensity-based models. We assume the point process driving the credit events is composed of a systematic and an idiosyncratic component, whose intensities are independently specified by a mean-reverting affine jump-diffusion process with self-exciting jumps. The proposed framework is competent of capturing the feedback effect. We further demonstrate how the proposed framework can be used to price synthetic collateralized debt obligation (CDO). Finally, we present the sensitivity analysis to demonstrate the effect of different parameters governing the contagion effect on the spread of tranches and the expected loss of the CDO.","PeriodicalId":50447,"journal":{"name":"Finance and Stochastics","volume":"68 1","pages":"79 - 98"},"PeriodicalIF":1.7,"publicationDate":"2022-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88106374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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