Related papers: Explicit solutions for continuous time mean-varian…
This paper considers the mean variance portfolio management problem. We examine portfolios which contain both primary and derivative securities. The challenge in this context is due to portfolio's nonlinearities. The delta-gamma…
Management of a portfolio that includes an illiquid asset is an important problem of modern mathematical finance. One of the ways to model illiquidity among others is to build an optimization problem and assume that one of the assets in a…
One of the reasons that higher order moment portfolio optimization methods are not fully used by practitioners in investment decisions is the complexity that these higher moments create by making the optimization problem nonconvex. Many few…
In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton--Jacobi--Bellman~(HJB) equations in continuous time. In practice the continuous-time framework of stochastic…
We study a continuous-time portfolio optimization problem under an explicit constraint on the Deviation Conditional Value-at-Risk (DCVaR), defined as the difference between the CVaR and the expected terminal wealth. While the mean-CVaR…
In this paper we discuss a family of viscous Cahn-Hilliard equations with a non-smooth viscosity term. This system may be viewed as an approximation of a "forward-backward" parabolic equation. The resulting problem is highly nonlinear,…
In the present paper, we derive a closed-form solution of the multi-period portfolio choice problem for a quadratic utility function with and without a riskless asset. All results are derived under weak conditions on the asset returns. No…
We present a robust version of the life-cycle optimal portfolio choice problem in the presence of labor income, as introduced in Biffis, Gozzi and Prosdocimi ("Optimal portfolio choice with path dependent labor income: the infinite horizon…
In this paper, we investigate an interesting and important stopping problem mixed with stochastic controls and a \textit{nonsmooth} utility over a finite time horizon. The paper aims to develop new methodologies, which are significantly…
We consider the problem of portfolio optimization in a simple incomplete market and under a general utility function. By working with the associated Hamilton-Jacobi-Bellman partial differential equation (HJB PDE), we obtain a closed-form…
This paper is devoted to study the effects arising from imposing a value-at-risk (VaR) constraint in mean-variance portfolio selection problem for an investor who receives a stochastic cash flow which he/she must then invest in a…
We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily…
The Hamilton-Jacobi-Bellman equation arising from the optimal portfolio selection problem is studied by means of the maximal monotone operator method. The existence and uniqueness of a solution to the Cauchy problem for the nonlinear…
This paper revisits the classical Merton portfolio choice problem over infinite horizon for high risk aversion, addressing technical challenges related to establishing the existence and identification of optimal strategies. Traditional…
In this paper, our aim is to investigate necessary conditions for optimal investment. We model the wealth process by Backward differential stochastic equations (shortly for BSDE) with or without constraints on wealth and portfolio process.…
We study a selection problem for degenerate viscous Hamilton--Jacobi equations with convex Hamiltonians, in which the approximation procedure combines a nonlinear discounted approximation with a small potential perturbation. A key question…
This paper studies the time-inconsistent MV optimal stopping problem via a game-theoretic approach to find equilibrium strategies. To overcome the mathematical intractability of direct equilibrium analysis, we propose a vanishing…
We study optimal portfolio choice under Epstein-Zin recursive utility in the presence of general leverage constraints. We first establish that the optimal value function is the unique viscosity solution to the associated…
This article studies a portfolio optimization problem, where the market consisting of several stocks is modeled by a multi-dimensional jump-diffusion process with age-dependent semi-Markov modulated coefficients. We study risk sensitive…
In this paper, we consider the portfolio optimization problem in a financial market under a general utility function. Empirical results suggest that if a significant market fluctuation occurs, invested wealth tends to have a notable change…