Related papers: Forward Backward SDEs Systems for Utility Maximiza…

This paper investigates the problem of maximizing expected terminal utility in a (generically incomplete) discrete-time financial market model with finite time horizon. In contrast to the standard setting, a possibly non-concave utility…

This memoir presents a systematic study of the utility maximization problem of an investor in a constrained and unbounded financial market. Building upon the work of Hu et al. (2005) [Ann. Appl. Probab., 15, 1691--1712] in a bounded…

We study a practical optimization problems for venture capital investments and/or Research and Development (R&D) investments. The first problem is that, given the amount of the initial investment and the reward function at the initial…

Forward-backward stochastic differential equations (FBSDEs) have been generalized by introducing jumps for better capturing random phenomena, while the resulting FBSDEs are far more intricate than the standard one from every perspective. In…

We consider an optimal switching problem where the terminal reward depends on the entire control trajectory. We show existence of an optimal control by applying a probabilistic technique based on the concept of Snell envelopes. We then…

This paper studies indefinite stochastic linear-quadratic (LQ) optimal control for jump-diffusion systems with random coefficients. We construct an algebraic inverse flow from the zero-control base system, extract the semimartingale kernel…

We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real…

We consider a problem of optimal investment with intermediate consumption and random endowment in an incomplete semimartingale model of a financial market. We establish the key assertions of the utility maximization theory assuming that…

This paper investigates the problem of maximizing expected terminal utility in a discrete-time financial market model with a finite horizon under non-dominated model uncertainty. We use a dynamic programming framework together with…

In this paper, we present a probabilistic numerical method for a class of forward utilities in a stochastic factor model. For this purpose, we use the representation of dynamic consistent utilities with mean of ergodic Backward Stochastic…

This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the…

A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion…

This paper is concerned with a Stackelberg game of backward stochastic differential equations (BSDEs), where the coefficients of the backward system and the cost functionals are deterministic, and the control domain is convex. Necessary and…

We extend the notion of forward performance criteria to settings with random endowment in incomplete markets. Building on these results, we introduce and develop the novel concept of \textit{forward optimized certainty equivalent (forward…

We consider a utility-maximization problem in a general semimartingale financial model, subject to constraints on the number of shares held in each risky asset. These constraints are modeled by predictable convex-set-valued processes whose…

We study a stochastic control approach to managed futures portfolios. Building on the Schwartz 97 stochastic convenience yield model for commodity prices, we formulate a utility maximization problem for dynamically trading a single-maturity…

We address the Merton problem of maximizing the expected utility of terminal wealth using techniques from variational analysis. Under a general continuous semimartingale market model with stochastic parameters, we obtain a characterization…

We give explicit solutions for utility maximization of terminal wealth problem $u(X_T)$ in the presence of Knightian uncertainty in continuous time $[0,T]$ in a complete market. We assume there is uncertainty on both drift and volatility of…

We consider the optimal control problem of stochastic evolution equations in a Hilbert space under a recursive utility, which is described as the solution of a backward stochastic differential equation (BSDE). A very general maximum…

The Stackelberg game model, where a leader commits to a strategy and the follower best responds, has found widespread application, particularly to security problems. In the security setting, the goal is for the leader to compute an optimal…