A Duality Method for Optimal Consumption and Investment Under Short- Selling Prohibition. I. General Market Coefficients

A duality method for optimal consumption and investment under short-selling prohibition

Optimal Investment and Consumption in a Black–scholes Market with Lévy-driven Stochastic Coefficients

In this paper, we investigate an optimal investment and consumption problem for an investor who trades in a Black–Scholes financial market with stochastic coefficients driven by a non-Gaussian Ornstein–Uhlenbeck process. We assume that an agent makes investment and consumption decisions based on a power utility function. By applying the usual separation method in the variables, we are faced wit...

Duality in constrained optimal investment and consumption problems: a synthesis

These lectures are all about optimal investment/consumption problems, usually with some ‘imperfection’, such as transaction costs, or constraints on the permitted portfolios, or different interest rates for borrowing and lending, or margin requirements for borrowing, or even just incomplete markets. Some time ago, Karatzas, Lehoczky & Shreve (1987), and Cox & Huang (1989) realised that the use ...

Optimal consumption and investment for markets with random coefficients

We consider an optimal investment and consumption problem for a Black-Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamical programming approach leads to an investigation of the Hamilton Jacobi Bellman (HJB) equation which is a highly non linear partia...

Convex duality in optimal investment under illiquidity

We study the problem of optimal investment by embedding it in the general conjugate duality framework of convex analysis. This allows for various extensions to classical models of liquid markets. In particular, we obtain a dual representation for the optimum value function in the presence of portfolio constraints and nonlinear trading costs that are encountered e.g. in modern limit order market...