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We study the portfolio problem of maximizing the outperformance probability over a random benchmark through dynamic trading with a fixed initial capital. Under a general incomplete market framework, this stochastic control problem can be…
This paper investigates well posedness of utility maximization problems for financial markets where stock returns depend on a hidden Gaussian mean reverting drift process. Since that process is potentially unbounded, well posedness cannot…
This paper presents a new framework for Merton's optimal investment problem which uses the theory of Meyer $\sigma$-fields to allow for signals that possibly warn the investor about impending jumps. With strategies no longer predictable,…
This paper studies the problem of maximizing the expected utility of terminal wealth for a financial agent with an unbounded random endowment, and with a utility function which supports both positive and negative wealth. We prove the…
This paper examines an optimal investment problem in a continuous-time (essentially) complete financial market with a finite horizon. We deal with an investor who behaves consistently with principles of Cumulative Prospect Theory, and whose…
We study Merton's expected utility maximization problem in an incomplete market, characterized by a factor process in addition to the stock price process, where all the model primitives are unknown. The agent under consideration is a price…
This paper studies an optimal reinsurance problem for a utility-maximizing insurer, subject to the reinsurer's endogenous default and background risk. An endogenous default occurs when the insurer's contractual indemnity exceeds the…
In this paper we analyse a dynamic model of investment under uncertainty in a duopoly, in which each firm has an option to switch from the present market to a new market. We construct a subgame perfect equilibrium in mixed strategies and…
Optimization under uncertainty deals with the problem of optimizing stochastic cost functions given some partial information on their inputs. These problems are extremely difficult to solve and yet pervade all areas of technological and…
This article deals with the problem of optimal allocation of capital to corporate bonds in fixed income portfolios when there is the possibility of correlated defaults. Under fairly general assumptions for the distribution of the total net…
We introduce a general framework for Markov decision problems under model uncertainty in a discrete-time infinite horizon setting. By providing a dynamic programming principle we obtain a local-to-global paradigm, namely solving a local,…
We consider a discrete-time financial market model with finite time horizon and give conditions which guarantee the existence of an optimal strategy for the problem of maximizing expected terminal utility. Equivalent martingale measures are…
A drawdown constraint forces the current wealth to remain above a given function of its maximum to date. We consider the portfolio optimisation problem of maximising the long-term growth rate of the expected utility of wealth subject to a…
In this paper the utility optimization problem for a general insurance model is studied. The reserve process of the insurance company is described by a stochastic differential equation driven by a Brownian motion and a Poisson random…
We provide analytical results for a static portfolio optimization problem with two coherent risk measures. The use of two risk measures is motivated by joint decision-making for portfolio selection where the risk perception of the portfolio…
We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the…
This paper studies a continuous-time market {under stochastic environment} where an agent, having specified an investment horizon and a target terminal mean return, seeks to minimize the variance of the return with multiple stocks and a…
This paper extends the classical dividend problem by incorporating a novel, path-dependent mechanism of firm default. In the traditional framework, ruin occurs when the surplus process first reaches zero. In contrast, default in our model…
We consider the multi-period portfolio optimization problem with a single asset that can be held long or short. Due to the presence of transaction costs, maximizing the immediate reward at each period may prove detrimental, as frequent…
This paper revisits the classical Merton portfolio choice problem over infinite horizon for high risk aversion, addressing technical challenges related to establishing the existence and identification of optimal strategies. Traditional…