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On Novikov and arbitrage properties of multidimensional diffusion processes with exploding drift

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  • Stummer, Wolfgang

Abstract

We investigate properties of processes Xt which are weak solutions of multidimensional stochastic differential equations of the formdXt=b(t,Xt) dt+dWt.We show that under certain non-stochastic conditions the solution Xt itself satisfies a uniform Novikov property. Consequently, it will follow that under these assumptions the no arbitrage property of Xt can be obtained by applying the Girsanov theorem twice (in reverse directions). For the sake of illustration, some examples with exploding drifts b are presented.

Suggested Citation

  • Stummer, Wolfgang, 2000. "On Novikov and arbitrage properties of multidimensional diffusion processes with exploding drift," Statistics & Probability Letters, Elsevier, vol. 46(1), pages 43-51, January.
    • Handle: RePEc:eee:stapro:v:46:y:2000:i:1:p:43-51
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    References listed on IDEAS

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    1. Stummer, Wolfgang, 1997. "On exponential moments of two Brownian functionals," Statistics & Probability Letters, Elsevier, vol. 31(3), pages 233-237, January.
    2. Freddy Delbaen, 1992. "Representing Martingale Measures When Asset Prices Are Continuous And Bounded," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 107-130, April.
    3. Stummer, Wolfgang, 1998. "On bounded entropy of solutions of multi-dimensional stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 36(4), pages 327-336, January.
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    Cited by:

    1. Rogers, L. C. G. & Stummer, Wolfgang, 2000. "Consistent fitting of one-factor models to interest rate data," Insurance: Mathematics and Economics, Elsevier, vol. 27(1), pages 45-63, August.

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