Long run risk sensitive portfolio with general factors

In the paper portfolio optimization over long run risk sensitive criterion is considered. It is assumed that economic factors which stimulate asset prices are ergodic but non necessarily uniformly ergodic. Solution to suitable Bellman equation using local span contraction with weighted norms is shown. The form of optimal strategy is presented and examples of market models satisfying imposed assumptions are shown.

[1]  Wolfgang J. Runggaldier,et al.  Connections between stochastic control and dynamic games , 1996, Math. Control. Signals Syst..

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

[3]  Terry J. Lyons,et al.  Stochastic finance. an introduction in discrete time , 2004 .

[4]  R. C. Merton,et al.  AN INTERTEMPORAL CAPITAL ASSET PRICING MODEL , 1973 .

[5]  Ł. Stettner,et al.  On additive and multiplicative (controlled) Poisson equations , 2006 .

[6]  Tomasz R. Bielecki,et al.  Dynamic Limit Growth Indices in Discrete Time , 2013 .

[7]  Tomasz R. Bielecki,et al.  Economic Properties of the Risk Sensitive Criterion for Portfolio Management , 2003 .

[8]  Andrzej Ruszczynski,et al.  Two-stage portfolio optimization with higher-order conditional measures of risk , 2012, Ann. Oper. Res..

[9]  Lukasz Stettner,et al.  Risk-Sensitive Control of Discrete-Time Markov Processes with Infinite Horizon , 1999, SIAM J. Control. Optim..

[10]  Lukasz Stettner,et al.  Risk sensitive portfolio optimization , 1999, Math. Methods Oper. Res..

[11]  S. Meyn,et al.  Spectral theory and limit theorems for geometrically ergodic Markov processes , 2002, math/0209200.

[12]  M. Kupper,et al.  Representation results for law invariant time consistent functions , 2009 .

[13]  Hans U. Gerber,et al.  An introduction to mathematical risk theory , 1982 .

[14]  Klaus Obermayer,et al.  A Unified Framework for Risk-sensitive Markov Decision Processes with Finite State and Action Spaces , 2011, ArXiv.

[15]  W. Fleming,et al.  Risk-Sensitive Control of Finite State Machines on an Infinite Horizon I , 1997 .

[16]  D. Hernández-Hernández,et al.  A characterization of the optimal risk-sensitive average cost in finite controlled Markov chains , 2005, math/0503478.

[17]  O. Hernández-Lerma Adaptive Markov Control Processes , 1989 .

[18]  Jonathan C. Mattingly,et al.  Yet Another Look at Harris’ Ergodic Theorem for Markov Chains , 2008, 0810.2777.

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

[20]  Zhao Zhang,et al.  Dynamic Coherent Acceptability Indices and Their Applications to Finance , 2010 .

[21]  S. Marcus,et al.  Risk sensitive control of Markov processes in countable state space , 1996 .

[22]  Dilip B. Madan,et al.  New Measures for Performance Evaluation , 2007 .

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

[24]  O. Hernández-Lerma,et al.  Further topics on discrete-time Markov control processes , 1999 .

[25]  L. Stettner,et al.  Remarks on Risk Neutral and Risk Sensitive Portfolio Optimization , 2006 .