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A Diffusion Model for Long-Term Optimization in the Presence of Stochastic Interest and Inflation Rates

Author

Listed:
  • Farid Mkaouar

    (Ecole Nationale d’Assurance (Enass))

  • Jean-Luc Prigent

    (Université de Cergy-Pontoise (THEMA) and Labex MME-DII)

  • Ilyes Abid

    (Institut Supérieur de Commerce de Paris)

Abstract

We consider the long term portfolio management problem, under stochastic rates and inflation risk. Five basic financial assets are considered: a money market account (the cash), an inflation-protected cash, a financial stock index and two different bonds with constant maturity. The first one corresponds to a nominal bond while the second one is an inflation-indexed bond. We consider constant maturation bonds, which allows to obtain a bond/stock ratio increasing with time (when there exists no inflation). This nice property is in accordance with popular advice. In this framework, we provide the general solution of the expected utility maximization. This intertemporal optimization problem is solved by using the martingale approach. We detail in particular the CRRA case. We determine also the optimal portfolio weights and analyze the solutions. We show in particular that the weight invested on the inflation-indexed bond increases with the relative risk aversion and also when the time horizon increases, which corresponds to a stronger demand for inflation hedging for longer maturities. Such feature illustrates the importance of introducing inflation-indexed bonds on financial markets.

Suggested Citation

  • Farid Mkaouar & Jean-Luc Prigent & Ilyes Abid, 2019. "A Diffusion Model for Long-Term Optimization in the Presence of Stochastic Interest and Inflation Rates," Computational Economics, Springer;Society for Computational Economics, vol. 54(1), pages 367-417, June.
    • Handle: RePEc:kap:compec:v:54:y:2019:i:1:d:10.1007_s10614-017-9742-0
    DOI: 10.1007/s10614-017-9742-0
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    More about this item

    Keywords

    Portfolio optimization; Stochastic interest rate; Stochastic inflation; Inflation-indexed bonds;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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