Related papers: Time consistent portfolio strategies for a general…
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…
This paper focuses on a class of continuous-time controlled Markov chains with time-inconsistent and distribution-dependent cost functional (in some appropriate sense). A new definition of time-inconsistent distribution-dependent…
The most commonly accepted model for investors' preferences is expected utility theory. More recently, other theories have emerged and pose new challenges to mathematics. The present paper treats preferences of cumulative prospect theory…
We analyze the efficiency of markets with friction, particularly power markets. We model the market as a dynamic system with $(d_t;\,t\geq 0)$ the demand process and $(s_t;\,t\geq 0)$ the supply process. Using stochastic differential…
We study Markowitz's mean-variance portfolio selection problem in a continuous-time Black-Scholes market with different borrowing and saving rates. The associated Hamilton-Jacobi-Bellman equation is fully nonlinear. Using a delicate partial…
This paper studies a dynamic optimal reinsurance and dividend-payout problem for an insurance company in a finite time horizon. The goal of the company is to maximize the expected cumulative discounted dividend payouts until bankruptcy or…
A dynamic model of collective consumption and saving decisions made by a finite number of agents with constant but different discount rates is developed. Collective utility is a weighted sum of individual utilities with time-varying utility…
We explore a decomposition in which returns on a large class of portfolios relative to the market depend on a smooth non-negative drift and changes in the asset price distribution. This decomposition is obtained using general continuous…
We introduce a modification of Perron's method, where semi-solutions are considered in a carefully defined asymptotic sense. With this definition, we can show, in a rather elementary way, that in a zero-sum game or a control problem (with…
In an incomplete continuous-time securities market with uncertainty generated by Brownian motions, we derive closed-form solutions for the equilibrium interest rate and market price of risk processes. The economy has a finite number of…
We investigate a continuous-time investment-consumption problem with model uncertainty in a general diffusion-based market with random model coefficients. We assume that a power utility investor is ambiguity-averse, with the preference to…
In a reinforcement learning (RL) framework, we study the exploratory version of the continuous time expected utility (EU) maximization problem with a portfolio constraint that includes widely-used financial regulations such as short-selling…
In this paper we investigate possible approaches to study general time-inconsistent optimization problems without assuming the existence of optimal strategy. This leads immediately to the need to refine the concept of time-consistency as…
We consider the game-theoretic approach to time-inconsistent stopping of a one-dimensional diffusion where the time-inconsistency is due to the presence of a non-exponential (weighted) discount function. In particular, we study (weak)…
In this paper we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial…
This paper formulates a model of utility for a continuous time framework that captures the decision-maker's concern with ambiguity about both volatility and drift. Corresponding extensions of some basic results in asset pricing theory are…
In this paper we consider an interval portfolio selection problem with uncertain returns and introduce an inclusive concept of satisfaction index for interval inequality relation. Based on the satisfaction index, we propose an approach to…
In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the…
We develop a framework for stochastic portfolio theory (SPT), which incorporates modern nonlinear price impact and impact decay models. Our main result is the derivation of the celebrated master formula for additive functional generation of…
Canonical models of Markov decision processes (MDPs) usually consider geometric discounting based on a constant discount factor. While this standard modeling approach has led to many elegant results, some recent studies indicate the…