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Portfolio Analysis of Financial Market Risks by Random Set Tools

Author

Listed:
  • Vorobyev, Oleg Yu.
  • Novosyolov, Arcady A.
  • Simonov, Konstantin V.
  • Fomin, Andrew

Abstract

A new approach to portfolio analysis of financial market risks by random set tools is considered. Despite many attempts, the consistent and global modeling of financial markets remains an open problem. In particular it remains a challenge to find a simple and tractable economic and probabilistic approach to market modeling. This paper attempts to highlight fundamental properties that a market model should possess. The paper suggests a random set approach as a probabilistic base of this model. Using this approach it is possible to establish a corresponding interactive market dynamics that involves a minimal number of sets. These sets include the set of capital surpluses, the set of capital within assets and the set of capital deficits. Several interesting properties related to random volatility of assets quality, probabilities of quality categories and defaults and matrices of transition probabilities of switching among categories can be derived. In addition the random set approach allows to derive the so called transition set-matrices, random set invariants of capital redistribution processes. Empirical evidence will be given that confirm these random set findings. The approach is also illustrated by collapses in U.S. financial markets in 90's and can be used to explain Russian default'98.

Suggested Citation

  • Vorobyev, Oleg Yu. & Novosyolov, Arcady A. & Simonov, Konstantin V. & Fomin, Andrew, 2001. "Portfolio Analysis of Financial Market Risks by Random Set Tools," MPRA Paper 16756, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:16756
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    References listed on IDEAS

    as
    1. Martin S. Fridson, 1991. "What Went Wrong With The Highly Leveraged Deals?," Journal of Applied Corporate Finance, Morgan Stanley, vol. 4(3), pages 57-67, September.
    2. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    3. Scott D. Aguais & Anthony M. Santomero, 1997. "Incorporating New Fixed Income Approaches into Commercial Loan Valuation," Center for Financial Institutions Working Papers 98-06, Wharton School Center for Financial Institutions, University of Pennsylvania.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    risk; financial market; portfolio analysis; random set; Set-at-Risk;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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