Skip to main content
×
Home
    • Aa
    • Aa

Optimal Stopping Problems for Asset Management

  • Savas Dayanik (a1) and Masahiko Egami (a2)
Abstract

An asset manager invests the savings of some investors in a portfolio of defaultable bonds. The manager pays the investors coupons at a constant rate and receives a management fee proportional to the value of the portfolio. He/she also has the right to walk out of the contract at any time with the net terminal value of the portfolio after payment of the investors' initial funds, and is not responsible for any deficit. To control the principal losses, investors may buy from the manager a limited protection which terminates the agreement as soon as the value of the portfolio drops below a predetermined threshold. We assume that the value of the portfolio is a jump diffusion process and find an optimal termination rule of the manager with and without protection. We also derive the indifference price of a limited protection. We illustrate the solution method on a numerical example. The motivation comes from the collateralized debt obligations.

Copyright
Corresponding author
Postal address: Departments of Industrial Engineering and Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey. Email address: sdayanik@bilkent.edu.tr
∗∗ Postal address: Graduate School of Economics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan. Email address: egami@econ.kyoto-u.ac.jp
References
Hide All
[1] AsmussenS., AvramF. and PistoriusM. R. (2004). Russian and American put options under exponential phase-type Lévy models. Stoch. Process. Appl. 109, 79111.
[2] BorodinA. N. and SalminenP. (2002). Handbook of Brownian Motion—Facts and Formulae, 2nd edn. Birkhäuser, Basel.
[3] BoyarchenkoS. I. and LevendorskiıˇS. Z. (2002). Perpetual American options under Lévy processes. SIAM J. Control Optimization 40, 16631696.
[4] ÇinlarE. (2006). Jump-diffusions. Blackwell-Tapia Conference, 3–4 November 2006. Avalaible at http://www.ima.umn.edu/2006-2007/SW11.3-4.06/abstracts.html#Cinlar-Erhan.
[5] ChanT. (1999). Pricing contingent claims on stocks driven by Lévy processes. Ann. Appl. Prob. 9, 504528.
[6] ColwellD. B. and ElliottR. J. (2006). Discontinuous asset prices and non-attainable contingent claims. Math. Finance 3, 295308.
[7] ContR. and TankovP. (2004). Financial Modelling with Jump Processes. Chapman & Hall/CRC, Boca Raton, FL.
[8] DavisM. H. A. (1984). Piecewise-deterministic Markov processes: a general class of nondiffusion stochastic models. J. R. Statist. Soc. Ser. B 46, 353388.
[9] DavisM. H. A. (1993). Markov Models and Optimization (Monogr. Statist. Appl. Prob. 49). Chapman & Hall, London.
[10] DayanikS. (2008). Optimal stopping of linear diffusions with random discounting. Math. Operat. Res. 33, 645661.
[11] DayanikS. and KaratzasI. (2003). On the optimal stopping problem for one-dimensional diffusions. Stoch. Process. Appl. 107, 173212.
[12] DayanikS. and SezerS. (2009). Multisource Bayesian sequential hypothesis testing. Preprint.
[13] DayanikS., PoorH. V. and SezerS. O. (2008). Multisource Bayesian sequential change detection. Ann. Appl. Prob. 18, 552590.
[14] Di NunnoG., ØksendalB. and ProskeF. (2009). Malliavin Calculus for Lévy Processes with Applications to Finance. Springer, Berlin.
[15] DuffieD. (1996). Dynamic Asset Pricing Theory. Princeton University Press.
[16] DuffieD. and GârleanuN. (2001). Risk and valuation of collateralized debt obligations. Financial Anal. J. 57, 4159.
[17] DuffieD. and SingletonK. J. (1999). Modeling term structures of defaultable bonds. Rev. Financial Stud. 12, 687720.
[18] EgamiM. and EsteghamatK. (2006). An approximation method for analysis and valuation of credit correlation derivatives. J. Banking Finance 30, 341364.
[19] HullJ. and WhiteA. (2004). Valuation of a CDO and an n th to default CDS without Monte Carlo simulation. J. Derivatives 12, 823.
[20] KarlinS. and TaylorH. M. (1981). A Second Course in Stochastic Processes. Academic Press, New York.
[21] KouS. G. and WangH. (2004). Option pricing under a double exponential Jump diffusion model. Manag. Sci. 50, 11781192.
[22] LelandH. E. (1994). Corporate debt value, bond covenants, and optimal capital structure. J. Finance 49, 12131252.
[23] LucasD. J., GoodmanL. S. and FabozziF. J. (2006). Collateralized Debt Obligations: Structures and Analysis. John Wiley, Hoboken, NJ.
[24] MordeckiE. (1999). Optimal stopping for a diffusion with Jumps. Finance Stoch. 3, 227236.
[25] MordeckiE. (2002). Optimal stopping and perpetual options for Lévy processes. Finance Stoch. 6, 473493.
[26] PhamH. (1997). Optimal stopping, free boundary, and American option in a Jump-diffusion model. Appl. Math. Optimization 35, 145164.
[27] SchoutensW. (2003). Lévy Processes in Finance: Pricing Financial Derivatives. John Wiley, Chichester.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Advances in Applied Probability
  • ISSN: 0001-8678
  • EISSN: 1475-6064
  • URL: /core/journals/advances-in-applied-probability
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords:

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 9 *
Loading metrics...

Abstract views

Total abstract views: 70 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 19th October 2017. This data will be updated every 24 hours.