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2071. Stochastic Ito-Volterra integral equations arising in finance: a streamlined numerical approach
Invited abstract in session WC-39: Financial Modelling, stream Stochastic Modelling.
Wednesday, 12:30-14:00Room: 35 (building: 306)
Authors (first author is the speaker)
| 1. | Antonio Luciano Martire
|
| MEMOTEF, Sapienza University of Rome | |
| 2. | Immacolata Oliva
|
| Methods and Models for Economics, Territory and Finance, Sapienza University of Rome |
Abstract
In recent years, stochastic integral equations of Volterra type have been employed as modelling tools for financial, economic, and demographic problems. In such a perspective, it is well known that a nonlinear stochastic Ito–Volterra integral equation is well-known model widely used simulating stock and electricity prices. Unfortunately, these kinds of equations do not allow closed-form solutions, but require the use of numerical methods to obtain suitable approximations. In this paper, we present a feasible, fast, and accurate numerical algorithm to evaluate the unknown solution of such equations. We mainly exploit the Lipschitz condition, which needs to be assumed in order to ensure the existence and uniqueness of the solution of this kind of equations, and a particular version of the mean value theorem for stochastic integrals. We also provide an extensive convergence analysis for our proposal.
Keywords
- Algorithms
- Stochastic Models
Status: accepted
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