Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values

Date

2017-08-03

Author

Sezer, Ali Devin
Popıer, Alexandre

Metadata

Show full item record

Item Usage Stats

124
views

0
downloads

We solve a class of BSDE with a power function f(y) = y q , q > 1, driving its drift and with the terminal boundary condition ξ = ∞ · 1B(m,r) c (for which q > 2 is assumed) or ξ = ∞ · 1B(m,r) , where B(m, r) is the ball in the path space C([0, T]) of the underlying Brownian motion centered at the constant function m and radius r. The solution involves the derivation and solution of a related heat equation in which f serves as a reaction term and which is accompanied by singular and discontinuous Dirichlet boundary conditions. Although the solution of the heat equation is discontinuous at the corners of the domain the BSDE has continuous sample paths with the prescribed terminal value.

URI

https://hdl.handle.net/11511/77317

Conference Name

Workshop on Stochastic processes - Actuarial science and Finance

Collections

Graduate School of Applied Mathematics, Conference / Seminar

Suggestions

OpenMETU
Core

Backward stochastic differential equations with non-Markovian singular terminal values Sezer, Ali Devin; Popier, Alexandre (2019-04-01) We solve a class of BSDE with a power function f (y) = y(q), q > 1, driving its drift and with the terminal boundary condition xi = infinity . 1( B(m,r)c )(for which q > 2 is assumed) or xi = infinity . 1B(m,r), where B(m, r) is the ball in the path space C([0,T]) of the underlying Brownian motion centered at the constant function m and radius r. The solution involves the derivation and solution of a related heat equation in which f serves as a reaction term and which is accompanied by singular and disconti...
Nonlocal hydrodynamic type of equations Gürses, Metin; Pekcan, Asli; Zheltukhın, Kostyantyn (Elsevier BV, 2020-06-01) We show that the integrable equations of hydrodynamic type admit nonlocal reductions. We first construct such reductions for a general Lax equation and then give several examples. The reduced nonlocal equations are of hydrodynamic type and integrable. They admit Lax representations and hence possess infinitely many conserved quantities.
Integrable KdV systems: Recursion operators of degree four Gurses, M; Karasu, Atalay (1999-01-25) The recursion operator and bi-Hamiltonian formulation of the Drinfeld-Sokolov system are given. (C) 1999 Elsevier Science B.V.
Explicit evaluation of Walsh transforms of a class of Gold type functions Cosgun, Ayhan (2018-03-01) Let K = F-2(k) denote the finite field of 2(k) elements. The Walsh transform of a class of Gold type functions f(x) = Tr-K (x(2a+1) + x(2b+1)), 0 <= a < b at alpha is an element of K is determined in recent results of Lahtonen et al. (2007) [7], Roy (2012) [10] and Cosgun et al. (2016) [2] under some restrictions on k, a, b and a. In this paper, we give explicit evaluation of the Walsh transforms off without any restriction on k, a, b and alpha. Therefore we improve and generalize the related results in lit...
Cyclic codes and reducible additive equations Guneri, Cem; Özbudak, Ferruh (Institute of Electrical and Electronics Engineers (IEEE), 2007-02-01) We prove a Weil-Serre type bound on the number of solutions of a class of reducible additive equations over finite fields. Using the trace representation of cyclic codes, this enables us to write a general estimate for the weights of cyclic codes. We extend Woffmann's weight bound to a larger classes of cyclic codes. In particular, our result is applicable to any cyclic code over F-p and F-p2, where p is an arbitrary prime. Examples indicate that our bound performs very well against the Bose-Chaudhuri-Hocqu...

Citation Formats

A. D. Sezer and A. Popıer, “Backward Stochastic Differential Equations with Nonmarkovian Singular Terminal Values,” presented at the Workshop on Stochastic processes - Actuarial science and Finance, 2017, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/77317.