# STAR seminars - STochastics And Risk

This series of webinars addresses all interested people in probability, stochastic analysis, control, risk evaluation, statistics, with a view towards applications, in particular to renewable energy markets and production. This series brings together the major research themes of the projects STORM, SCROLLER, and SPATUS

The webinars will take place on Zoom and a link to the virtual room will be sent out in advance to all members of the Section Risk and Stochastics as well as to all those who registered at the registration page.

Friday 15th. January, Time 11.00-12.00 (45 min seminar, Q&A and coffee break).

Speaker: Arne Bang Huseby - University of Oslo

Title: Optimal reinsurance contracts in the multivariate case

Abstract: An insurance contract implies that risk is ceded from ordinary policy holders to companies.  However, companies do the same thing between themselves.  This is known as reinsurance, and the ceding company is known as the cedent.  The rationale could be the same; i.e., that a financially weaker agent is passing risk to a stronger one. In reality even the largest companies do this to diversify risk, and financially the cedent may be as strong as the reinsurer.  The problem of determining re­in­su­rance contracts which are optimal with respect to some reasonable criterion has been studied extensively within actuarial science.  Different contact types are considered such as stop-loss contracts where the reinsurance company covers risk above a certain level, and insurance layer contracts where the reinsurance company covers risk within an interval.  The contracts are then optimized with respect to some risk measure, such as value-at risk (VaR) or conditional tail expectation (CTE). In this seminar we consider the problem of minimizing VaR in the case of multiple insurance layer contracts.  Such contracts are known to be optimal in the univariate case, and the optimal contract is easily determined.  In the multivariate case, however, finding the optimal set of contracts is not easy.  In fact the optimal contract is not even unique in this case.  Still by considering solutions where the risk is balanced between the contracts, a solution can be found using an iterative Monte Carlo method.

Upcoming

Friday 29th. January, Time 11.00-12.00 (45 min seminar, Q&A and coffee break).

Speaker: Josep Vives - University of Barcelona

Title: Decomposition and high order approximation of option prices. Some applications to Heston, Bates, CEV and rough volatility models.

Abstract:

Using Itô calculus techniques we present an option price decomposition for local and stochastic volatility jump diffusion models and we use it to obtain fast and accurate approximations of call option prices for different local or stochastic volatility models.

The main purpose is to present the ideas given in the recent papers

A. Gulisashvili, M. Lagunas, R. Merino and J. Vives (2020): “Higher order approximation of call option prices in stochastic volatility models”. Journal of Computational Finance 24 (1).

But I will also comment ideas of the papers:

E. Alòs, R. De Santiago and J. Vives (2015): “Calibration of stochastic volatility models via second order approximation: the Heston case”. International Journal of Theoretical and Applied Finance 18 (6): 1550036 (31 pages).

J. Vives (2016): “Decomposition of the pricing formula for stochastic volatility models based on Malliavin – Skorohod type calculus”. Proocedings of the Research School CIMPA-UNESCO-MSER-MINECO-MOROCCO on Statistical Methods and Applications in Actuarial Science and Finance 2013. Springer.

R. Merino and J. Vives (2017): “Option price decomposition in local volatility models and some Applications”. International Journal of Stochastic Analysis. Volume 2017, Article ID 8019498, 16 pages

R. Merino, J. Pospísil, T. Sobotka and J. Vives (2018): “Decomposition formula for jump diffusion models”. International Journal of Theoretical and Applied Finance 21 (8).

R. Merino, J. Pospisil, T. Sobotka, T. Sottinen and J. Vives (2021): “Decomposition formula for rough Volterra stochastic volatility models”. Submitted.

Friday 12th. February, Time 11.00-12.00 (45 min seminar, Q&A and coffee break).

Speaker: Emil R. Framnes - Global Head of Trading Norges Bank Investment Management

Title: TBA

Abstract: TBA

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Previous seminars in Spring 2021

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Link to: Past seminars - Fall 2020

Published Aug. 28, 2020 10:34 AM - Last modified Jan. 15, 2021 10:46 AM