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Reflected backward stochastic differential equations in an orthant

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Abstract

We consider RBSDE in an orthant with oblique reflection and with time and space dependent coefficients, viz.

$$Z(t) = \xi + \int_t^T {b(s, Z(s))} ds + \int_t^T {R(s, Z(s))} dY(s) - \int_t^T {\left\langle {U(s), dB(s)} \right\rangle } $$

with Zi(·)≥0, Yi(·) nondecreasing and Yi(·) increasing only when Zi(·) = 0, 1 ≤i ≤d. Existence of a unique solution is established under Lipschitz continuity ofb, R and a uniform spectral radius condition onR. On the way we also prove a result concerning the variational distance between the ‘pushing parts’ of solutions of auxiliary one-dimensional problem.

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  1. Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile, Mysore Road, 560 059, Bangalore, India

    S. Ramasubramanian

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  1. S. Ramasubramanian
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Ramasubramanian, S. Reflected backward stochastic differential equations in an orthant. Proc. Indian Acad. Sci. (Math. Sci.) 112, 347–360 (2002). https://doi.org/10.1007/BF02829759

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  • DOI: https://doi.org/10.1007/BF02829759

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