Discrete‐time risk sensitive portfolio optimization with proportional transaction costs

Pitera, Marcin; Stettner, Łukasz

doi:10.1111/mafi.12406

Cited by 7 publications

(7 citation statements)

References 49 publications

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“…Risk-seeking behavior of agents (e.g investors) is examined theoretically and empirically by many previous studies in the literature (e.g. [2][3][4][5][6][7][8][9][10][11]). Specifically, Seel and Strack [5] show that, in a declining industry, risk-loving agents might invest in projects with negative expected returns.…”

Section: Motivation: the Presence Of Risk-seekersmentioning

confidence: 99%

“…Let's consider Roulette, which is a popular casino game. In this game, players choose to place finite bets on either a single integer number (from 1 to 36) or a group of several numbers, which are low (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18), high (19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30)(31)(32)(33)(34)(35)(36), odd, even, black, or red on a wheel. The number zero might appear once (French/European style roulette) or twice (American style roulette) on the wheel and it is colored in green.…”

Section: Gamblers As Risk-seekersmentioning

confidence: 99%

“…Note that the parameter γ i can be positive or negative: γ i > 0 represents the case of risk aversion while γ i < 0 captures the case of risk-seeking behavior. Here, the relative competition θ i ∈ [−1, 1] is a constant and it indicates that agent i takes into account her performance by comparison to her peers 11 .…”

Section: The N-agent Gamesmentioning

confidence: 99%

“…Theorem 17 (Convergence). The MFE (24) and (49) are the limits as n → ∞ of n-player Nash equilibria (11) and (38), respectively.…”

Section: Convergence Of Nash Equilibria To Mfementioning

confidence: 99%

“…The reason is because there is a one-to-one mapping between the case of including and excluding the agent i of the optimization problem(8) 10. Many previous studies in the literature examine long-term investment strategies, for example Siegel[59] 11. In the utility function (6) the relative performance parameter θi can be negative, positive, or zero.…”

mentioning

confidence: 99%

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Finite and mean field games for optimal investment with HARA utility function and the presence of risk-seeking agents

Nguyen

2024

Preprint

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This study extends the work of Lacker and Zariphopoulou LZ19 by considering the financial market with the presence of both risk-averse and risk-seeking agents. Specifically, the n-agent (finite) and mean field games for optimal investment with the family of the hyperbolic absolute risk aversion (HARA) utility function under relative performance concern/motivation are studied. Several specific forms of the HARA family, including exponential, power, and logarithmic form are investigated. We prove that there exists a unique constant Nash equilibrium and a unique constant mean field equilibrium in both the n-agent and mean field games for the case of strictly concave utility function. For the case of strictly convex utility function, there exists a unique corner solution in these games where agents invest all of their wealth in risky assets (e.g. stock) and invest nothing on riskless assets (e.g. bond). Furthermore, we discuss the qualitative effects of the personal and market coefficients on the optimal investment strategies.

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Section: Motivation: the Presence Of Risk-seekersmentioning

confidence: 99%

Section: Gamblers As Risk-seekersmentioning

confidence: 99%

Section: The N-agent Gamesmentioning

confidence: 99%

“…Theorem 17 (Convergence). The MFE (24) and (49) are the limits as n → ∞ of n-player Nash equilibria (11) and (38), respectively.…”

Section: Convergence Of Nash Equilibria To Mfementioning

confidence: 99%

mentioning

confidence: 99%

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Finite and mean field games for optimal investment with HARA utility function and the presence of risk-seeking agents

Nguyen

2024

Preprint

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Markov decision processes with risk-sensitive criteria: an overview

Bäuerle,

Jaśkiewicz

2024

Math Meth Oper Res

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The paper provides an overview of the theory and applications of risk-sensitive Markov decision processes. The term ’risk-sensitive’ refers here to the use of the Optimized Certainty Equivalent as a means to measure expectation and risk. This comprises the well-known entropic risk measure and Conditional Value-at-Risk. We restrict our considerations to stationary problems with an infinite time horizon. Conditions are given under which optimal policies exist and solution procedures are explained. We present both the theory when the Optimized Certainty Equivalent is applied recursively as well as the case where it is applied to the cumulated reward. Discounted as well as non-discounted models are reviewed.

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On asymptotic convergence rate of random search

Tarłowski

2023

J Glob Optim

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This paper presents general theoretical studies on asymptotic convergence rate (ACR) for finite dimensional optimization. Given the continuous problem function and discrete time stochastic optimization process, the ACR is the optimal constant for control of the asymptotic behaviour of the expected approximation errors. Under general assumptions, condition ACR$$<1$$ < 1 implies the linear behaviour of the expected time of hitting the $$\varepsilon $$ ε - optimal sublevel set with $$\varepsilon \rightarrow 0^+ $$ ε → 0 + and determines the upper bound for the convergence rate of the trajectories of the process. This paper provides general characterization of ACR and, in particular, shows that some algorithms cannot converge linearly fast for any nontrivial continuous optimization problem. The relation between asymptotic convergence rate in the objective space and asymptotic convergence rate in the search space is provided. Examples and numerical simulations with use of a (1+1) self-adaptive evolution strategy and other algorithms are presented.

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Discrete‐time risk sensitive portfolio optimization with proportional transaction costs

Cited by 7 publications

References 49 publications

Finite and mean field games for optimal investment with HARA utility function and the presence of risk-seeking agents

Finite and mean field games for optimal investment with HARA utility function and the presence of risk-seeking agents

Markov decision processes with risk-sensitive criteria: an overview

On asymptotic convergence rate of random search

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