Diffusions, Markov Processes, and Martingales by L. C. G. Rogers

By L. Rogers, David Williams. 2000

1,481 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/76a0bf804659d925ec7e33ca1c6b2cd820009ac1

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Citations in the corpus

Risk Minimization with Incomplete Information in a Model for High‐Frequency Data (2000, methodology): “We denote for any measurable stochastic process U on ( ,F, P ) by (o,FS)U (respectively by (p,FS)U ) the optional projection (respectively the predictable projection) of U on the filtration {FSt } (see, e.g., Rogers and Williams 1987, Chap.”
Root's barrier: Construction, optimality and applications to variance options. (2011, background): “This result connects Root’s problem and the obstacle problem under a smoothness assumption on the function u. However, ideally we want a oneto-one correspondence. We know from the results of Rost (1976) that there always exists a solution to SEP(σ, ν, μ), and from Loynes (1970) that the solution is ”
A Representation for Non-Colliding Random Walks (2002, methodology): “Thus, by standard Doob-Hunt theory (see, for example, [10, 34]) if we can show that, with probability one, N(t)/t → (1, .”
Affine processes are regular (2009, methodology): “As an immediate Corollary to this theorem, every stochastically continuous affine process has a càdlàg version, see for instance Rogers and Williams (1994).”
Stochastic Risk Premiums, Stochastic Skewness in Currency Options, and Stochastic Discount Factors in International Economies (2008, methodology): “We useXh to summarize the uncertainty in economyh and represent the state-price deflator via the fol- lowing multiplicative decomposition (withM h0 = 1): M ht = exp ( − Z t 0 rhs ds ) E ( − Z t 0 γhs dX h s ) , h = 1,2, . . . ,N, (1) whererht denotes the instantaneous interest rate in economyh, γht…”