Search results for "Merton's portfolio problem"

showing 3 items of 3 documents

A Unified Approach to Portfolio Optimization with Linear Transaction Costs

2004

In this paper we study the continuous time optimal portfolio selection problem for an investor with a finite horizon who maximizes expected utility of terminal wealth and faces transaction costs in the capital market. It is well known that, depending on a particular structure of transaction costs, such a problem is formulated and solved within either stochastic singular control or stochastic impulse control framework. In this paper we propose a unified framework, which generalizes the contemporary approaches and is capable to deal with any problem where transaction costs are a linear/piecewise-linear function of the volume of trade. We also discuss some methods for solving numerically the p…

Structure (mathematical logic)Transaction costMathematical optimizationComputer sciencejel:C63General Mathematicsjel:C61Function (mathematics)Management Science and Operations ResearchSingular controljel:G11Merton's portfolio problemEconomicsPortfolioPortfolio optimizationportfolio choice transaction costs stochastic singular control stochastic impulse control computational methodsSoftwareExpected utility hypothesisSSRN Electronic Journal
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Portfolio optimisation with strictly positive transaction costs and impulse control

1998

One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a non…

Statistics and ProbabilityTransaction costMathematical optimizationExponential utilityMerton's portfolio problemReplicating portfolioEconomicsPortfolio optimisation transaction costs impulse control asymptotic analysis.PortfolioOptimal stoppingStatistics Probability and UncertaintyPortfolio optimizationFinanceModern portfolio theory
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A Portfolio Problem with Uncertainty

2000

In this paper we present two models for cash flow matching with an uncertain level of payments at each due date. To solve the problem of minimising the initial investment we use the scenario method proposed by Dembo, and the robust optimisation method proposed by Mulvey et al. We unify these optimisation methods in a general co-ordinated model that guarantees a match under every scenario. This general model is also a multi-objective programming problem. We illustrate this methodology in a problem with several scenarios.

Matching (statistics)Mathematical optimizationSuperhedging priceComputer scienceFinancial economicsMerton's portfolio problemPortfolioCash flowPortfolio optimizationBlack–Litterman modelModern portfolio theory
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