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May 2015

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Seminari di Eckhard Platen all'Università di Firenze
by Giacomo Scandolo 04 May '15

04 May '15

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 ============================================================= 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. ============================================================= 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. --- Questa e-mail è priva di virus e malware perché è attiva la protezione avast! Antivirus. http://www.avast.com

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Annuncio di seminario
by Tiziano Vargiolu 04 May '15

04 May '15

ANNUNCIO DI SEMINARIO Il Prof. Eckhard Platen, professore alla University of Technology di Sydney ed attuale Presidente della Bachelier Finance Society, terra' il seguente seminario dalle 14.30 alle 15.30 del martedi' 5 maggio in aula 2BC60 del Dipartimento di Matematica, via Trieste 63, Padova. (Si noti lo spostamento dalla originale aula 2AB40 alla 2BC60) Referente: W. Runggaldier __________________ TITLE: BENCHMARKED RISK MINIMIZATION ABSTRACT: The paper discusses the problem of hedging not perfectly replicable contingent claims by using a benchmark, the numeraire portfolio, as reference unit. The proposed concept of benchmarked risk minimization generalizes classical risk minimization, pioneered by Foellmer, Sondermann and Schweizer. The latter relies on a quadratic criterion, requesting the square integrability of contingent claims and the existence of an equivalent risk neutral probability measure. The proposed concept of benchmarked risk minimization avoids these restrictive assumptions. It employs the real world probability measure as pricing measure and identifies the minimal possible price for the hedgeable part of a contingent claim. Furthermore, the resulting benchmarked profit and loss is only driven by nontraded uncertainty and forms a martingale that starts at zero. Benchmarked profit and losses, when pooled and sufficiently independent, become in total negligible. This property is highly desirable from a risk management point of view. It is making asymptotically benchmarked risk minimization the least expensive method for pricing and hedging of an increasing number of not fully replicable benchmarked contingent claims. (Joint work with Ke Du.)

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