Ricordo che il Prof. Eckhard PLATEN (University of Technology, Sydney)
questa settimana terrà due seminari presso il Dipartimento di Scienze per l'Economia e l'Impresa Edificio D6, via delle Pandette, 32, Firenze
Tutti gli interessati sono invitati a partecipare
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Giovedì 7 Maggio, 10.00-12.00, aula D6/105
''Numerical Solutions of Stochastic Differential Equations with Jumps in Finance ''
Abstract. In financial and actuarial modelling and other areas of application, stochastic differential equations with jumps have been employed to describe the dynamics of various state variables. The numerical solution of such equations is more complex than that of those only driven by Brownian motions. The aim of this lecture is to present various numerical methods used in quantitative finance for models involving stochastic differential equations with jumps. It emphasises mathematical concepts, techniques and intuition crucial for modern numerical methods in derivative pricing and risk management. Questions of numerical stability and convergence will be discussed. Several recent results will be presented on higher-order methods for scenario and Monte Carlo simulation, including implicit, predictor corrector and extrapolation methods.
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Venerdì 8 Maggio, 10.00-12.00, aula D6/013
"A Benchmark Approach to Finance "
Abstract. This lecture introduces into the benchmark approach, which provides a generalized framework for financial market modelling. It allows for a unified treatment of derivative pricing, portfolio optimization and risk management. It extends beyond the classical asset pricing theories, with significant differences emerging for extreme maturity contracts and risk measures relevant to pensions and insurance. The Law of the Minimal Price will be presented for derivative pricing. A Naïve Diversification Theorem allows forming a proxy for the numeraire portfolio. The richer modelling framework of the benchmark approach leads to the derivation of tractable, realistic models under the real world probability measure. It will be explained how the approach differs from the classical risk neutral approach. Examples on long term and extreme maturity derivatives demonstrate the important fact that a range of contracts can be less expensively priced and hedged than suggested by classical theory.
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