Optimal lifetime consumption and investment under a drawdown constraint

We consider the infinite-horizon optimal consumption-investment problem under a drawdown constraint, i.e., when the wealth process never falls below a fixed fraction of its running maximum. We assume that the risky asset is driven by the with constant coefficients. For a general class of utility functions, we provide the value function in explicit form and derive closed-form expressions for the optimal consumption and investment strategy.

[1]  R. C. Merton,et al.  Optimum Consumption and Portfolio Rules in a Continuous-Time Model* , 1975 .

[2]  KaratzasIoannis,et al.  Optimal portfolio and consumption decisions for a small investor on a finite horizon , 1987 .

[3]  W. Schachermayer.  Optimal investment in incomplete markets when wealth may become negative , 2001 .

[4]  H. Soner,et al.  Modeling continuous-time financial markets with capital gains taxes , 2007 .

[5]  R. C. Merton,et al.  Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case , 1969 .

[6]  J. Cox,et al.  Optimal consumption and portfolio policies when asset prices follow a diffusion process , 1989 .

[7]  H. He,et al.  Labor income, borrowing constraints, and equilibrium asset prices , 1993 .

[8]  S. Shreve,et al.  Methods of Mathematical Finance , 2010 .

[9]  Hervé Roche.  Optimal Consumption and Investment Strategies under Wealth Ratcheting , 2006 .

[10]  G. Constantinides,et al.  Portfolio selection with transactions costs , 1976 .

[11]  H. Soner,et al.  Optimal Investment and Consumption with Transaction Costs , 1994 .

[12]  Ioannis Karatzas,et al.  Brownian Motion and Stochastic Calculus , 1987 .

[13]  Jakša Cvitanić,et al.  Convex Duality in Constrained Portfolio Optimization , 1992 .

[14]  Monique Jeanblanc,et al.  Optimization of consumption with labor income , 1998, Finance Stochastics.

[15]  Jakša Cvitanić,et al.  On portfolio optimization under "drawdown" constraints , 1994 .

[16]  Sanford J. Grossman,et al.  OPTIMAL INVESTMENT STRATEGIES FOR CONTROLLING DRAWDOWNS , 1993 .

[17]  W. Schachermayer,et al.  The asymptotic elasticity of utility functions and optimal investment in incomplete markets , 1999 .

[18]  S. Shreve,et al.  Optimal portfolio and consumption decisions for a “small investor” on a finite horizon , 1987 .

[19]  P. Protter.  Stochastic integration and differential equations , 1990 .

[20]  Guy Barles,et al.  Optimal Control on the $L^\infty$ Norm of a Diffusion Process , 1994 .

[21]  A. R. Norman,et al.  Portfolio Selection with Transaction Costs , 1990, Math. Oper. Res..

[22]  Krzysztof Nowicki,et al.  The Grossman and Zhou investment strategy is not always optimal , 2005 .