Long-term optimal portfolios with floor

Long-term risk-sensitive portfolio optimization is studied with floor constraint. A simple rule to characterize its solution is mentioned under a general setting. Following this rule, optimal portfolios are constructed in several ways, using the optimal portfolio without floor constraint, combined with ideas of dynamic portfolio insurance, such as CPPI (constant proportion portfolio insurance), OBPI (option-based portfolio insurance), and DFP (dynamic fund protection). In addition, examples are presented with explicit computations of solutions.

[1]  W. Fleming,et al.  Risk‐Sensitive Control and an Optimal Investment Model , 2000 .

[2]  A. Shiryaev,et al.  Limit Theorems for Stochastic Processes , 1987 .

[3]  W. Sharpe,et al.  Dynamic Strategies for Asset Allocation , 1988 .

[4]  N. Karoui,et al.  Optimal portfolio management with American capital guarantee , 2005 .

[5]  Tomasz R. Bielecki,et al.  Risk-sensitive ICAPM with application to fixed-income management , 2004, IEEE Transactions on Automatic Control.

[6]  G. Wise,et al.  Continuity of filtrations of sigma algebras , 1987 .

[7]  David C. Flaspohler,et al.  Mathematics of finance , 1973 .

[8]  Huyên Pham,et al.  A large deviations approach to optimal long term investment , 2003, Finance Stochastics.

[9]  R. C. Merton,et al.  Optimum consumption and portfolio rules in a continuous - time model Journal of Economic Theory 3 , 1971 .

[10]  W. Fleming,et al.  Risk‐Sensitive Control and an Optimal Investment Model , 2000 .

[11]  Mark H. A. Davis,et al.  Risk-sensitive benchmarked asset management , 2008 .

[12]  F. Black,et al.  Theory of constant proportion portfolio insurance , 1992 .

[13]  H. Hata,et al.  Solving long term optimal investment problems with Cox-Ingersoll-Ross interest rates , 2006 .

[14]  I. Karatzas On the pricing of American options , 1988 .

[15]  H. Nagai Asymptotics of the probability of minimizing ‘down-side’ risk under partial information , 2011 .

[16]  Jean-Luc Prigent,et al.  Portfolio Optimization and Performance Analysis , 2007 .

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

[18]  Hideo Nagai,et al.  Optimal Strategies for Risk-Sensitive Portfolio Optimization Problems for General Factor Models , 2002, SIAM J. Control. Optim..

[19]  Nicole El Karoui,et al.  APPLICATION TO AMERICAN OPTIONS AND PORTFOLIO INSURANCE By , 2008 .

[20]  Hans U. Gerber,et al.  Pricing Dynamic Investment Fund Protection , 2000 .

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

[22]  K. Bichteler Stochastic Integration with Jumps , 2002 .

[23]  Jun Sekine,et al.  A note on long-term optimal portfolios under drawdown constraints , 2006, Advances in Applied Probability.

[24]  S. Peng,et al.  Risk-Sinsitive Dynamic Portfolio Optimization with Partial Information on Infinite Time Horizon , 2002 .

[25]  Jean-Luc Prigent,et al.  Portfolio Insurance Strategies: OBPI Versus CPPI , 2001 .

[26]  P. Boyle,et al.  Dynamic Fund Protection , 2001 .

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

[28]  S. Sheu,et al.  Asymptotics of the probability minimizing a "down-side" risk , 2010, 1001.2131.

[29]  W. Fleming,et al.  Optimal long term growth rate of expected utility of wealth , 1999 .

[30]  Huyên Pham,et al.  A risk-sensitive control dual approach to a large deviations control problem , 2003, Syst. Control. Lett..

[31]  Larry A Shepp,et al.  A New Look at Pricing of the ”Russian Option“ , 1995 .

[32]  H. Gerber,et al.  MARTINGALE APPROACH TO PRICING PERPETUAL AMERICAN OPTIONS ON TWO STOCKS , 1996 .

[33]  H. Nagai,et al.  Risk-sensitive portfolio optimization on infinite time horizon , 2002 .

[34]  J. L. Pedersen,et al.  Discounted optimal stopping problems for the maximum process , 2000, Journal of Applied Probability.

[35]  Fischer Black,et al.  Simplifying portfolio insurance , 1987 .

[36]  H. Föllmer,et al.  Optional decompositions under constraints , 1997 .

[37]  Hans U. Gerber A.S.A.,et al.  Pricing Perpetual Fund Protection with Withdrawal Option , 2003 .

[38]  Donald L. Luskin,et al.  Portfolio insurance : a guide to dynamic hedging , 1988 .

[39]  Hans Föllmer,et al.  Optional decomposition and Lagrange multipliers , 1997, Finance Stochastics.

[40]  Hiroaki Hata,et al.  A risk-sensitive stochastic control approach to an optimal investment problem with partial information , 2006, Finance Stochastics.

[41]  Alʹbert Nikolaevich Shiri︠a︡ev,et al.  Optimal Stopping and Free-Boundary Problems , 2006 .

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

[43]  N. El Karoui,et al.  CONSTRAINED OPTIMIZATION WITH RESPECT TO STOCHASTIC DOMINANCE: APPLICATION TO PORTFOLIO INSURANCE , 2006 .

[44]  S. Pliska,et al.  Risk-Sensitive Dynamic Asset Management , 1999 .

[45]  Alex W. H. Chan Merton, Robert C. , 2010 .