Related papers: Singular Perturbation Expansion for Utility Maximi…
We consider a dynamic portfolio optimization problem that incorporates predictable returns, instantaneous transaction costs, price impact, and stochastic volatility, extending the classical results of Garleanu and Pedersen (2013), which…
We consider the classical Merton problem of lifetime consumption-portfolio optimization problem with small proportional transaction costs. The first order term in the asymptotic expansion is explicitly calculated through a singular ergodic…
In this short note, we consider mean-variance optimized portfolios with transaction costs. We show that introducing quadratic transaction costs makes the optimization problem more difficult than using linear transaction costs. The reason…
In the context of the multi-dimensional infinite horizon optimal consumption-investment problem with proportional transaction costs, we provide the first order expansion in small transact costs. Similar to the one-dimensional derivation in…
We consider a utility maximization problem for an investment-consumption portfolio when the current utility depends also on the wealth process. Such kind of problems arise, e.g., in portfolio optimization with random horizon or with random…
This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider the optimal allocation of wealth among multiple…
Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment…
In this note we consider the maximization of the expected terminal wealth for the setup of quadratic transaction costs. First, we provide a very simple probabilistic solution to the problem. Although the problem was largely studied, as far…
In this paper, we first conduct a study of the portfolio selection problem, incorporating both exogenous (proportional) and endogenous (resulting from liquidity risk, characterized by a stochastic process) transaction costs through the…
The aim of this short note is to establish a limit theorem for the optimal trading strategies in the setup of the utility maximization problem with proportional transaction costs. This limit theorem resolves the open question from [4]. The…
This paper concerns the numerical solution of the finite-horizon Optimal Investment problem with transaction costs under Potential Utility. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints. In…
We reconsider the problem of optimal trading in the presence of linear and quadratic costs, for arbitrary linear costs but in the limit where quadratic costs are small. Using matched asymptotic expansion techniques, we find that the trading…
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…
In this paper, we consider the portfolio optimization problem in a financial market where the underlying stochastic volatility model is driven by n-dimensional Brownian motions. At first, we derive a Hamilton-Jacobi-Bellman equation…
We consider the portfolio optimisation problem where the terminal function is an S-shaped utility applied at the difference between the wealth and a random benchmark process. We develop several numerical methods for solving the problem…
Transaction costs play a critical role in asset allocation and consumption strategies in portfolio management. We apply the methods of dynamic programming and singular perturbation expansion to derive the closed-form leading solutions to…
We revisit the optimal investment and consumption problem with proportional transaction costs. We prove that both the value function and the slopes of the lines demarcating the no-trading region are analytic functions of cube root of the…
In an incomplete model, where under an appropriate num\'eraire, the stock price process is driven by a sigma-bounded semimartingale, we investigate the behavior of the expected utility maximization problem under small perturbations of the…
We propose a general approximation method for determining optimal trading strategies in markets with proportional transaction costs, with a polynomial approximation of the residual value function. The method is exemplified by several…
We assume a continuous-time price impact model similar to Almgren-Chriss but with the added assumption that the price impact parameters are stochastic processes modeled as correlated scalar Markov diffusions. In this setting, we develop…