Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-08T11:43:09.776Z Has data issue: false hasContentIssue false
  • English
  • Français

Markov decision process algorithms for wealth allocation problems with defaultable bonds

Part of: Mathematical finance

Published online by Cambridge University Press:  10 June 2016

Iker Perez ,
David Hodge  and
Huiling Le
Iker Perez*
Affiliation:
The University of Nottingham
David Hodge*
Affiliation:
The University of Nottingham
Huiling Le*
Affiliation:
The University of Nottingham
*
* Current address: Horizon Digital Economy Research, The University of Nottingham, Geospatial Building, Triumph Road, Nottingham NG7 2TU, UK. Email address: iker.perez@nottingham.ac.uk
** Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK.
** Postal address: School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we are concerned with analysing optimal wealth allocation techniques within a defaultable financial market similar to Bielecki and Jang (2007). We study a portfolio optimization problem combining a continuous-time jump market and a defaultable security; and present numerical solutions through the conversion into a Markov decision process and characterization of its value function as a unique fixed point to a contracting operator. In this paper we analyse allocation strategies under several families of utility functions, and highlight significant portfolio selection differences with previously reported results.

Keywords

Portfolio optimizationdefaultable bondMarkov decision process

MSC classification

Primary: 91G10: Portfolio theory
Secondary: 90C40: Markov and semi-Markov decision processes
Type
Research Article
Information
Advances in Applied Probability , Volume 48 , Issue 2 , June 2016 , pp. 392 - 405
Copyright
Copyright © Applied Probability Trust 2016 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Almudevar, A. (2001).A dynamic programming algorithm for the optimal control of piecewise deterministic Markov processes.SIAM J. Control Optimization. 40,525–539.CrossRefGoogle Scholar
[2]Bäuerle, N. and Rieder, U. (2009).MDP algorithms for portfolio optimization problems in pure jump markets.Finance Stoch. 13,591–611.CrossRefGoogle Scholar
[3]Bäuerle, N. and Rieder, U. (2010).Optimal control of piecewise deterministic Markov processes with finite time horizon. In Modern Trends in Controlled Stochastic Processes: Theory and Applications,Luniver,Frome, pp.123–143.Google Scholar
[4]Bäuerle, N. and Rieder, U. (2011).Markov Decision Processes with Applications to Finance.Springer,Heidelberg.Google Scholar
[5]Bertsekas, D. P. and Shreve, S. E. (1978).Stochastic Optimal Control.Academic Press,New York.Google Scholar
[6]Bielecki, T. R. and Jang, I. (2006).Portfolio optimization with a defaultable security.Asia–Pacific Financial Markets 13,113–127.Google Scholar
[7]Bielecki, T. R. and Rutkowski, M. (2002).Credit Risk: Modelling, Valuation and Hedging.Springer,Berlin.Google Scholar
[8]Bo, L.,Wang, Y. and Yang, X. (2010).An optimal portfolio problem in a defaultable market.Adv. Appl. Prob. 42,689–705.Google Scholar
[9]Capponi, A. and Figueroa-López, J. E. (2014).Dynamic portfolio optimization with a defaultable security and regime-switching.Math. Finance 24,207–249.Google Scholar
[10]Duffie, D. and Singleton, K. J. (1999).Modelling term structures of defaultable bonds.Rev. Financial Studies 12,687–720.Google Scholar
[11]Fleming, W. H. and Pang, T. (2004).An application of stochastic control theory to financial economics.SIAM J. Control Optimization 43,502–531.CrossRefGoogle Scholar
[12]Jeanblanc, M.,Yor, M. and Chesney, M. (2009).Mathematical Methods for Financial Markets.Springer,London.CrossRefGoogle Scholar
[13]Karatzas, I. and Shreve, S. E. (1998).Methods of Mathematical Finance.Springer,New York.Google Scholar
[14]Kirch, M. and Runggaldier, W. J. (2004).Efficient hedging when asset prices follow a geometric Poisson process with unknown intensities.SIAM J. Control Optimization 43,1174–1195.CrossRefGoogle Scholar
[15]Lakner, P. and Liang, W. (2007).Optimal investment in a defaultable bond.Math. Financial Econom. 1,283–310.CrossRefGoogle Scholar
[16]Merton, R. C. (1969).Lifetime portfolio selection under uncertainty: the continuous-time case.Rev. Econom. Statist. 51,247–257.CrossRefGoogle Scholar
[17]Pham, H. (2002).Smooth solutions to optimal investment models with stochastic volatilities and portfolio constraints.Appl. Math. Optimization 46,55–78.Google Scholar
[18]Puterman, M. L. (1994).Markov Decision Processes: Discrete Stochastic Dynamic Programming.John Wiley,New York.Google Scholar