The Risk and Stochastics Seminar aims to promote communication and discussion of research in the mathematics of insurance and finance and their interface, to encourage interaction between practice and theory in these areas, and to support academically students in related programmes at postgraduate level. All are welcome to attend. Sessions run regularly during LSE terms, and will place on Thursdays at 5.00pm (unless otherwise stated below) in COL 6.15.
The current up-to-date schedule is given below. Please contact Events for further information about any of these seminars. All are very welcome to attend.
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30th May 2013
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Mikhail Urusov (University of Duisburg-Essen) 16.00-17.00. OLD 3.28
Title: On the boundary behaviour of diffusions and the martingale property of the associated local martingales
Abstract: Link to PDF
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15th May 2013
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Michael Schroeder (TBA) 15.00- 16.30 OLD 1.29
Title: Mechanisms for no-arbitrage term-structure modelling with applications to interest-rates and realized-variance.
Abstract: Suppose that the sentiment is changing in some financial market, or that conditions have changed recently. Examples include volatility levels which are expected to change, or interest-rates expected to be adjusted.
How do we quantify the effects of these changes on derivatives positions. We will discuss mechanisms for the construction of `no-arbitrage' term structures which enable this; these retain tractability in valuing derivatives and comply with stylized facts like mean-reversion and positivity of rates. This will be illustrated in a paradigm valuation of typical fixed-income derivatives.
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4th October 2012
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Mingyu Xu (Chinese Academy of Sciences) 16.00hrs-17.00hrs
Title: BSDE with a ratio constraint and its application
Abstract: Non-linear backward stochastic differential equations (BSDEs in short) were first studied by Pardoux and Peng (1990), who proved the existence and uniqueness of the adapted solution, under smooth square integrability assumptions on the coefficient and the terminal condition, and when the coefficient $g(t,\omega ,y,z)$ is Lipschitz in $(y,z)$ uniformly in $(t,\omega )$. From then on, the theory of backward stochastic differential equations (BSDE) has been widely and rapidly developed. And many problems in mathematical finance can be treated as BSDEs. The natural connection between BSDE and partial differential equations (PDE) of parabolic and elliptic types is also important applications. In this talk, we study a new development of BSDE, BSDE with ratio constraint, i.e. portfolio process is controlled by a function of wealth process. The existence and uniqueness results are presented and we will give some application of this kind of BSDE at last.
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20th September 2012
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Elisa Alòs (Universitat Pompeu Fabra)
Title :A decomposition formula for option prices in the Heston model and applications to option pricing approximation
Abstract: By means of classical Itôs calculus we decompose option prices as the sum of the classical Black-Scholes formula with volatility parameter equal to the root-mean-square future average volatility plus a term due to correlation and a term due to the volatility of the volatility. This decomposition allows us to develop first and second-order approximation formulas for option prices and implied volatilities in the Heston volatility framework, as well as to study their accuracy for short maturities. Numerical examples are given.
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