Related papers: An extended Merton problem with relaxed benchmark …
This paper develops a time-inconsistent and path-dependent singular control framework incorporating a running minimum process. We derive a verification theorem that characterizes equilibria under substantially weaker regularity conditions…
This paper provides a dual formulation of the optimal consumption problem with internal multiplicative habit formation. In this problem, the agent derives utility from the ratio of consumption to the internal habit component. Due to this…
Solving stochastic optimal control problems with quadratic control costs can be viewed as approximating a target path space measure, e.g. via gradient-based optimization. In practice, however, this optimization is challenging in particular…
This paper studies the optimal consumption under the addictive habit formation preference in markets with transaction costs and unbounded random endowments. To model the proportional transaction costs, we adopt the Kabanov's multi-asset…
In this paper, we are concerned with the optimization of a dynamic investment portfolio when the securities which follow a multivariate Merton model with dependent jumps are periodically invested and proceed by approximating the…
This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…
By the calculus of Peng's G-sublinear expectation and G-Brownian motion on a sublinear expectation space $(\Omega, {\cal H}, \hat{\mathbb{E}})$, we first set up an optimality principle of stochastic control problem. Then we investigate an…
This paper studies some unconventional utility maximization problems when the ratio type relative portfolio performance is periodically evaluated over an infinite horizon. Meanwhile, the agent is prohibited from short-selling stocks. Our…
We propose martingale consumption as a natural, desirable consumption pattern for any given (proportional) investment strategy. The idea is to always adjust current consumption so as to achieve level expected future consumption under the…
In this article we study a multi-asset version of the Merton investment and consumption problem with proportional transaction costs. In general it is difficult to make analytical progress towards a solution in such problems, but we…
An innovative extension of Geometric Brownian Motion model is developed by incorporating a weighting factor and a stochastic function modelled as a mixture of power and trigonometric functions. Simulations based on this Modified Brownian…
We study a static portfolio optimization problem with two risk measures: a principle risk measure in the objective function and a secondary risk measure whose value is controlled in the constraints. This problem is of interest when it is…
This paper is concerned with the stochastic recursive optimal control problem with mixed delay. The connection between Pontryagin's maximum principle and Bellman's dynamic programming principle is discussed. Without containing any…
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…
We consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk…
In this paper, we investigate the optimal management of defined contribution (abbr. DC) pension plan under relative performance ratio and Value-at-Risk (abbr. VaR) constraint. Inflation risk is introduced in this paper and the financial…
The classical quadratic regulator problem has rarely been studied for systems with persistent memory until recent times. In this paper we study the quadratic tracking problem on a \emph{ finite time horizon} for a system described by a…
The "standard" Merton formulation of optimal investment and consumption involves optimizing the integrated lifetime utility of consumption, suitably discounted, together with the discounted future bequest. In this formulation the utility of…
We propose a new approach to utilities that is consistent with state-dependent utilities. In our model utilities reflect the level of consumption satisfaction of flows of cash in future times as they are valued when the economic agents are…
This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cram{\'e}r-Lundberg…