Displaying similar documents to “Robust portfolio selection under exponential preferences”

Risk minimizing strategies for a portfolio of interest-rate securities

Andrzej Palczewski (2008)

Banach Center Publications

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The paper presents an application of stochastic control methods to fixed income management in an incomplete market with external economic factors. The objective of an investor is the minimization of a shortfall risk. The problem is reduced to the multidimensional Bellman equation. It is shown that for a large class of loss functions the equation possesses a continuous solution. We also consider loss functions from the HARA class and prove that for such functions the Hamilton-Jacobi-Bellman...

A pension fund in the accumulation phase: a stochastic control approach

Salvatore Federico (2008)

Banach Center Publications

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In this paper we propose and study a continuous time stochastic model of optimal allocation for a defined contribution pension fund in the accumulation phase. The level of wealth is constrained to stay above a "solvency level". The fund manager can invest in a riskless asset and in a risky asset, but borrowing and short selling are prohibited. The model is naturally formulated as an optimal stochastic control problem with state constraints and is treated by the dynamic programming approach....

Optimal investment under stochastic volatility and power type utility function

Benchaabane, Abbes, Benchettah, Azzedine (2011)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 37F21, 70H20, 37L40, 37C40, 91G80, 93E20. In this work we will study a problem of optimal investment in financial markets with stochastic volatility with small parameter. We used the averaging method of Bogoliubov for limited development for the optimal strategies when the small parameter of the model tends to zero and the limit for the optimal strategy and demonstrated the convergence of these optimal strategies.

A note on 'Big Match'

Jean-Michel Coulomb (2010)

ESAIM: Probability and Statistics

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We present a very simple proof of the existence of the value for 'Big Match' first shown by Blackwell and Ferguson (1968).

Nash equilibrium payoffs for stochastic differential games with reflection

Qian Lin (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper, we investigate Nash equilibrium payoffs for nonzero-sum stochastic differential games with reflection. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for nonzero-sum stochastic differential games with nonlinear cost functionals defined by doubly controlled reflected backward stochastic differential equations.

Differential games of partial information forward-backward doubly SDE and applications

Eddie C. M. Hui, Hua Xiao (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper addresses a new differential game problem with forward-backward doubly stochastic differential equations. There are two distinguishing features. One is that our game systems are initial coupled, rather than terminal coupled. The other is that the admissible control is required to be adapted to a subset of the information generated by the underlying Brownian motions. We establish a necessary condition and a sufficient condition for an equilibrium point of nonzero-sum games...

Existence of Nash equilibria in two-person stochastic games of resource extraction

P. Szajowski (2006)

Banach Center Publications

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This paper deals with two-person stochastic games of resource extraction under both the discounted and the mean payoff criterion. Under some concavity and additivity assumptions concerning the payoff and the transition probability function a stationary Nash equilibrium is shown to exist. The proof is based on Schauder-Tychonoff's fixed point theorem, applied to a suitable payoff vector space.

Applications of time-delayed backward stochastic differential equations to pricing, hedging and portfolio management in insurance and finance

Łukasz Delong (2012)

Applicationes Mathematicae

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We investigate novel applications of a new class of equations which we call time-delayed backward stochastic differential equations. Time-delayed BSDEs may arise in insurance and finance in an attempt to find an investment strategy and an investment portfolio which should replicate a liability or meet a target depending on the strategy applied or the past values of the portfolio. In this setting, a managed investment portfolio serves simultaneously as the underlying security on which...

Target achieving portfolio under model misspecification: quadratic optimization framework

Dariusz Zawisza (2012)

Applicationes Mathematicae

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We incorporate model uncertainty into a quadratic portfolio optimization framework. We consider an incomplete continuous time market with a non-tradable stochastic factor. Two stochastic game problems are formulated and solved using Hamilton-Jacobi-Bellman-Isaacs equations. The proof of existence and uniqueness of a solution to the resulting semilinear PDE is also provided. The latter can be used to extend many portfolio optimization results.

A two armed bandit type problem revisited

Gilles Pagès (2010)

ESAIM: Probability and Statistics

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In Benaïm and Ben Arous (2003) is solved a multi-armed bandit problem arising in the theory of learning in games. We propose a short and elementary proof of this result based on a variant of the Kronecker lemma.

Hamilton–Jacobi equations and two-person zero-sum differential games with unbounded controls

Hong Qiu, Jiongmin Yong (2013)

ESAIM: Control, Optimisation and Calculus of Variations

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A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower Hamilton–Jacobi–Isaacs equations, respectively. Consequently, when the Isaacs’ condition is satisfied, the upper and lower value functions coincide, leading to the existence of the value function of the differential game. Due to the unboundedness of...

Weak infinitesimal operators and stochastic differential games.

Ramón Ardanuy, A. Alcalá (1992)

Stochastica

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This article considers the problem of finding the optimal strategies in stochastic differential games with two players, using the weak infinitesimal operator of process xi the solution of d(xi) = f(xi,t,u,u)dt + sigma(xi,t,u,u)dW. For two-person zero-sum stochastic games we formulate the minimax solution; analogously, we perform the solution for coordination and non-cooperative stochastic differential games.

Stochastic differential games involving impulse controls

Feng Zhang (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game.