Related papers: On the parabolic equation for portfolio problems
Portfolio selection problems that optimize expected utility are usually difficult to solve. If the number of assets in the portfolio is large, such expected utility maximization problems become even harder to solve numerically. Therefore,…
We consider a general discrete-time financial market with proportional transaction costs as in [Kabanov, Stricker and R\'{a}sonyi Finance and Stochastics 7 (2003) 403--411] and [Schachermayer Math. Finance 14 (2004) 19--48]. In addition to…
We consider a single-period portfolio selection problem for an investor, maximizing the expected ratio of the portfolio utility and the utility of a best asset taken in hindsight. The decision rules are based on the history of stock returns…
For a long investment time horizon, it is preferable to rebalance the portfolio weights at intermediate times. This necessitates a multi-period market model in which portfolio optimization is usually done through dynamic programming.…
In this paper, we consider the optimal portfolio liquidation problem under the dynamic mean-variance criterion and derive time-consistent solutions in three important models. We give adapted optimal strategies under a reconsidered…
We combine forward investment performance processes and ambiguity averse portfolio selection. We introduce the notion of robust forward criteria which addresses the issues of ambiguity in model specification and in preferences and…
The classical optimal investment and consumption problem with infinite horizon is studied in the presence of transaction costs. Both proportional and fixed costs as well as general utility functions are considered. Weak dynamic programming…
The mean-variance portfolio model, based on the risk-return trade-off for optimal asset allocation, remains foundational in portfolio optimization. However, its reliance on restrictive assumptions about asset return distributions limits its…
In this research, we present an analysis of the optimal investment, consumption, and life insurance acquisition problem for a wage earner with partial information. Our study considers the non-linear filter case where risky asset prices are…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
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 an infinite-horizon optimal investment, consumption and insurance problem for an economic agent who consumes a perishable and a durable good. The agent trades in a risk-free asset, a risky asset, and a durable good whose price…
This paper is dedicated to the analysis of infinite horizon optimal control problems subject to semilinear parabolic equations with constraints on the controls and discounted cost functionals. The discount factors on the cost and the state…
The main objective of this paper is to develop a martingale-type solution to optimal consumption--investment choice problems ([Merton, 1969] and [Merton, 1971]) under time-varying incomplete preferences driven by externalities such as…
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…
This paper introduces a dual problem to study a continuous-time consumption and investment problem with incomplete markets and stochastic differential utility. For Epstein-Zin utility, duality between the primal and dual problems is…
Path Integral Control methods were developed for stochastic optimal control covering a wide class of finite horizon formulations with control affine nonlinear dynamics. Characteristic for this class is that the HJB equation is linear and…
We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it is well known, one can map this problem into a linear programming setting. For some values of the external…
The paper investigates the consumption-investment problem for an investor with Epstein-Zin utility in an incomplete market. A non-Markovian environment with unbounded parameters is considered, which is more realistic in practical financial…
Managing insurance and financial risk when data is limited is a key task in the insurance industry. In this paper, we focus on cases where the risk distribution is modeled as a mixture with some components estimable to high precision or…