Related papers: Minimizing the Probability of Lifetime Drawdown un…
In this paper we provide a self-contained exposition of the problem of sustaining a constant consumption level in a Ramsey model. Our focus is on the case in which the output capital-ratio is random. After a brief review of the known…
We establish a rigorous duality theory, under No Unbounded Profit with Bounded Risk, for an infinite horizon problem of optimal consumption in the presence of an income stream that can terminate randomly at an exponentially distributed…
In this paper, we consider an optimal reinsurance problem to minimize the probability of drawdown for the scaled Cram\'er-Lundberg risk model when the reinsurance premium is computed according to the mean-variance premium principle. We…
Ergodicity describes an equivalence between the expectation value and the time average of observables. Applied to human behaviour, ergodic theories of decision-making reveal how individuals should tolerate risk in different environments. To…
We study optimal investment problems under the framework of cumulative prospect theory (CPT). A CPT investor makes investment decisions in a single-period financial market with transaction costs. The objective is to seek the optimal…
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…
We study an optimal control problem encompassing investment, consumption, and retirement decisions under exponential (CARA-type) utility. The financial market comprises a bond with constant drift and a stock following geometric Brownian…
We apply Blackwell optimality to repeated games. An equilibrium whose strategy profile is sequentially rational for all high enough discount factors simultaneously is a Blackwell (subgame-perfect, perfect public, etc.) equilibrium. The bite…
An investor trades a safe and several risky assets with linear price impact to maximize expected utility from terminal wealth. In the limit for small impact costs, we explicitly determine the optimal policy and welfare, in a general…
This paper studies a type of consumption preference where some adjustment costs are incured whenever the past spending maximum and the past spending minimum records are updated. This preference can capture the adverse effects of the…
We consider a stock that follows a geometric Brownian motion (GBM) and a riskless asset continuously compounded at a constant rate. We assume that the stock can go bankrupt, i.e., lose all of its value, at some exogenous random time…
In this paper, we propose a new class of optimization problems, which maximize the terminal wealth and accumulated consumption utility subject to a mean variance criterion controlling the final risk of the portfolio. The multiple-objective…
We investigate models of the life annuity insurance when the company invests its reserve into a risky asset with price following a geometric Brownian motion. Our main result is an exact asymptotic of the ruin probabilities for the case of…
We generalize classical results on the existence of optimal portfolios in discrete time frictionless market models to models with capital gains taxes. We consider the realistic but mathematically challenging rule that losses do not trigger…
We use a neural network to identify the optimal solution to a family of optimal investment problems, where the parameters determining an investor's risk and consumption preferences are given as inputs to the neural network in addition to…
We consider a financial market in which two securities are traded: a stock and an index. Their prices are assumed to satisfy the Black-Scholes model. Besides assuming that the index is a tradable security, we also assume that it is…
This paper develops a new model of business cycles. The model is economical in that it is solved with an aggregate demand-aggregate supply diagram, and the effects of shocks and policies are obtained by comparative statics. The model builds…
For the Ramsey model of economic growth, which describes the optimal allocation of consumption and saving over time, we assume the population dynamics to follow the Allee effect. The so-called Allee threshold separates two regimes from each…
We consider a model of optimal investment and consumption with both habit formation and partial observations in incomplete It\^{o} processes market. The investor chooses his consumption under the addictive habits constraint while only…
This paper studies finite-time optimal consumption-investment problems with power, logarithmic and exponential utilities, in a regime switching market with random coefficients, subject to coupled constraints on the consumption and…