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Value-Positivity for Matrix Games
- Krishnendu Chatterjee
  Krishnendu Chatterjee
  Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria;
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- Miquel Oliu-Barton
  Miquel Oliu-Barton
  CEREMADE, CNRS, Université Paris Dauphine-PSL University, 75016 Paris, France
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- Raimundo Saona
  Corresponding Author
  Raimundo Saona
  [email protected]
  https://orcid.org/0000-0001-5103-038X
  Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria;
  Correspondence
  Raimundo Saona, Institute of Science and Technology Austria, 3400 Klosterneuburg, Austria;
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Published Online:October 1, 2024
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Matrix games are the most basic model in game theory, and yet robustness with respect to small perturbations of the matrix entries is not fully understood. In this paper, we introduce value positivity and uniform value positivity, two properties that ...
Stochastic Control Problems with State Reflections Arising from Relaxed Benchmark Tracking
- Lijun Bo
  Lijun Bo
  School of Mathematics and Statistics, Xidian University, Xi’an 710126, China;
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- Yijie Huang
  Yijie Huang
  School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China;
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- Xiang Yu
  Corresponding Author
  Xiang Yu
  [email protected]
  https://orcid.org/0000-0003-4053-7876
  Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
  Correspondence
  Xiang Yu, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong
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Published Online:October 1, 2024
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This paper studies stochastic control problems motivated by optimal consumption with wealth benchmark tracking. The benchmark process is modeled by a combination of a geometric Brownian motion and a running maximum process, indicating its increasing trend ...
Comparison Between Mean-Variance and Monotone Mean-Variance Preferences Under Jump Diffusion and Stochastic Factor Model
- Yuchen Li
  Corresponding Author
  Yuchen Li
  [email protected]
  https://orcid.org/0000-0003-4176-7008
  Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
  Correspondence
  Yuchen Li, Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
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- Zongxia Liang
  Zongxia Liang
  Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China;
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- Shunzhi Pang
  Shunzhi Pang
  School of Economics and Management, Tsinghua University, Beijing 100084, China
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Published Online:September 23, 2024
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Abstract
This paper compares the optimal investment problems based on monotone mean-variance (MMV) and mean-variance (MV) preferences in a Lévy market with an untradable stochastic factor. It is an open question proposed by Trybuła and Zawisza. Using the dynamic ...
Online Estimation and Optimization of Utility-Based Shortfall Risk
- Vishwajit Hegde
  Vishwajit Hegde
  Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India;
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- Arvind Satish Menon
  Arvind Satish Menon
  Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India;
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- Prashanth L.A.
  Corresponding Author
  Prashanth L.A.
  [email protected]
  https://orcid.org/0000-0003-0362-6730
  Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India;
  Correspondence
  Prashanth L.A., Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India;
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- Krishna Jagannathan
  Krishna Jagannathan
  Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, Tamil Nadu 600036, India
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Published Online:September 16, 2024
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Abstract
Utility-based shortfall risk (UBSR) is a risk metric that is increasingly popular in financial applications, owing to certain desirable properties that it enjoys. We consider the problem of estimating UBSR in a recursive setting, in which samples from the ...
Dual Solutions in Convex Stochastic Optimization
- Teemu Pennanen
  Teemu Pennanen
  Department of Mathematics, King’s College London, London WC2R 2LS, United Kingdom;
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- Ari-Pekka Perkkiö
  Corresponding Author
  Ari-Pekka Perkkiö
  [email protected]
  https://orcid.org/0000-0002-9787-0330
  Mathematics Institute, Ludwig Maximilian University of Munich, 80333 Munich, Germany
  Correspondence
  Ari-Pekka Perkkiö, Mathematics Institute, Ludwig Maximilian University of Munich, 80333 Munich, Germany
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Published Online:September 12, 2024
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Abstract
This paper studies duality and optimality conditions for general convex stochastic optimization problems. The main result gives sufficient conditions for the absence of a duality gap and the existence of dual solutions in a locally convex space of random ...

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