Sandwiched SDEs with unbounded drift driven by Hölder noises. (English) Zbl 07779237
In this article, the authors study a stochastic differential equation with an unbounded drift and general Hölder continuous noise of order \(\lambda \in (0,1)\). It is found that the corresponding equation has a unique solution, which either remains above a continuous function or has continuous upper and lower bounds, depending on the specific form of the drift. Under mild assumptions on the noise, it is shown that the solution possesses moments of all orders. Additionally, a connection to the solution of a Skorokhod reflection problem is demonstrated. To illustrate the results and provide motivation for applications, two stochastic volatility models, considered as generalizations of the CIR and CEV processes, are proposed. The study is completed by presenting a numerical scheme for the solution.
Reviewer: Javad Asadzade (Famagusta)
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 60H35 | Computational methods for stochastic equations (aspects of stochastic analysis) |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 91G30 | Interest rates, asset pricing, etc. (stochastic models) |
Keywords:
sandwiched process; unbounded drift; Hölder continuous noise; numerical scheme; stochastic volatilitySoftware:
longmemoReferences:
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