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This paper studies a portfolio allocation problem, where the goal is to prescribe the wealth distribution at the final time. We study this problem with the tools of optimal mass transport. We provide a dual formulation which we solve by a…
In this paper we formulate and solve an optimal problem for Stochastic process with a regime absorbing state. The solution for this problem is obtained through a system of partial differential equations. The method is applied to obtain an…
Based on a point of view that solvency and security are first, this paper considers regular-singular stochastic optimal control problem of a large insurance company facing positive transaction cost asked by reinsurer under solvency…
We determine the optimal investment strategy of an individual who targets a given rate of consumption and who seeks to minimize the probability of going bankrupt before she dies, also known as {\it lifetime ruin}. We impose two types of…
An empirical analysis, suggested by optimal Merton dynamics, reveals some unexpected features of asset volumes. These features are connected to traders' belief and risk aversion. This paper proposes a trading strategy model in the optimal…
We consider the Merton problem of optimizing expected power utility of terminal wealth in the case of an unobservable Markov-modulated drift. What makes the model special is that the agent is allowed to purchase costly expert opinions of…
We study the sensitivity of the expected utility maximization problem in a continuous semi-martingale market with respect to small changes in the market price of risk. Assuming that the preferences of a rational economic agent are modeled…
We discuss an optimal investment, consumption and insurance problem of a wage earner under inflation. Assume a wage earner investing in a real money account and three asset prices, namely: a real zero coupon bond, the inflation-linked real…
The subject of this paper is an optimal consumption/optimal portfolio problem with transaction costs and with multiple risky assets. In our model the transaction costs take a special form in that transaction costs on purchases of one of the…
This paper studies the problem of maximizing expected utility from terminal wealth in a semi-static market composed of derivative securities, which we assume can be traded only at time zero, and of stocks, which can be traded continuously…
We consider a Ramsey model with several households with heterogeneous preferences who are able to borrow capital to each other. Since the capital constraints of one household then depends on the others' capital, one can no longer optimize…
One index satisfies the duality axiom if one agent, who is uniformly more risk-averse than another, accepts a gamble, the latter accepts any less risky gamble under the index. Aumann and Serrano (2008) show that only one index defined for…
We study investment and insurance demand decisions for an agent in a theoretical continuous-time expected utility maximization model that combines risky assets with an (exogenous) insurable background risk. This risk takes the form of a…
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic…
The Merton problem is the well-known stochastic control problem of choosing consumption over time, as well as an investment mix, to maximize expected constant relative risk aversion (CRRA) utility of consumption. Merton formulated the…
In this work we analytically solve an optimal retirement problem, in which the agent optimally allocates the risky investment, consumption and leisure rate to maximise a gain function characterised by a power utility function of consumption…
In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the…
This paper studies the topic of cost-efficiency in incomplete markets. A payoff is called cost-efficient if it achieves a given probability distribution at some given investment horizon with a minimum initial budget. Extensive literature…
In this paper, we study an optimal reinsurance-investment problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component. We assume that the…
This paper is devoted to study the optimal portfolio problem. Harry Markowitz's Ph.D. thesis prepared the ground for the mathematical theory of finance. In modern portfolio theory, we typically find asset returns that are modeled by a…