Related papers: State-dependent utility maximization in L\'evy mar…
Empirical studies indicate the existence of long range dependence in the volatility of the underlying asset. This feature can be captured by modeling its return and volatility using functions of a stationary fractional Ornstein--Uhlenbeck…
We propose an alternative approach for solving a number of well-studied optimal stopping problems for L\'evy processes. Instead of the usual method of guess-and-verify based on martingale properties of the value function, we suggest a more…
In this paper, a new method for solving the problem of optimal control of semi-Markov processes with finitely many states is considered. A new form of the assertion on an extremum of a liner-fractional integral functional given on a set of…
This work takes up the challenges of utility maximization problem when the market is indivisible and the transaction costs are included. First there is a so-called solvency region given by the minimum margin requirement in the problem…
This paper studies the problem of maximizing expected utility from terminal wealth combining a static position in derivative securities, which we assume can be traded only at time zero, with a traditional dynamic trading strategy in stocks.…
In this paper we provide a unifying energy-based approach to the modeling, analysis and control of power systems and markets, which is based on the port-Hamiltonian framework. Using a primal-dual gradient method applied to the social…
We study utility maximization for power utility random fields with and without intermediate consumption in a general semimartingale model with closed portfolio constraints. We show that any optimal strategy leads to a solution of the…
In this paper, we consider a financial market with assets exposed to some risks inducing jumps in the asset prices, and which can still be traded after default times. We use a default-intensity modeling approach, and address in this…
Monotone mean-variance (MMV) utility is the minimal modification of the classical Markowitz utility that respects rational ordering of investment opportunities. This paper provides, for the first time, a complete characterization of optimal…
We study an optimization problem for a portfolio with a risk-free, a liquid, and an illiquid risky asset. The illiquid risky asset is sold in an exogenous random moment with a prescribed liquidation time distribution. The investor prefers a…
In this paper we derive the exact solution of the multi-period portfolio choice problem for an exponential utility function under return predictability. It is assumed that the asset returns depend on predictable variables and that the joint…
In this article we consider the infinite-horizon Merton investment-consumption problem in a constant-parameter Black - Scholes - Merton market for an agent with constant relative risk aversion R. The classical primal approach is to write…
We study a problem of utility maximization under model uncertainty with information including jumps. We prove first that the value process of the robust stochastic control problem is described by the solution of a quadratic-exponential…
We consider a stochastic volatility model with jumps where the underlying asset price is driven by the process sum of a 2-dimensional Brownian motion and a 2-dimensional compensated Poisson process. The market is incomplete, resulting in…
We consider a discrete time financial market with proportional transaction costs under model uncertainty, and study a num\'eraire-based semi-static utility maximization problem with an exponential utility preference. The randomization…
This paper studies De Finetti's optimal dividend problem with capital injection under spectrally positive Markov additive models. Based on dynamic programming principle, we first study an auxiliary singular control problem with a final…
We establish dual attainment for the multimarginal, multi-asset martingale optimal transport (MOT) problem, a fundamental question in the mathematical theory of model-independent pricing and hedging in quantitative finance. Our main result…
This paper includes a proof of well-posedness of an initial-boundary value problem involving a system of degenerate non-local parabolic PDE which naturally arises in the study of derivative pricing in a generalized market model. In a…
In this paper we consider a variation of the Merton's problem with added stochastic volatility and finite time horizon. It is known that the corresponding optimal control problem may be reduced to a linear parabolic boundary problem under…
In this paper, we study an intertemporal utility maximization problem in which an investor chooses consumption and portfolio strategies in the presence of a stochastic factor and a no-borrowing constraint. In the spirit of the Kim-Omberg…