Past Mathematical Finance Internal Seminar

28 February 2013
13:00
Gechun Liang
Abstract
In this talk, We show that both reflected BSDE and its associated penalized BSDE admit both optimal stopping representation and optimal control representation. We also show that both multidimensional reflected BSDE and its associated multidimensional penalized BSDE admit optimal switching representation. The corresponding optimal stopping problems for penalized BSDE have the feature that one is only allowed to stop at Poisson arrival times.
  • Mathematical Finance Internal Seminar
21 February 2013
13:00
Raphael Hauser
Abstract
We consider the problem of optimizing a portfolio of medium to low frequency quant strategies under heavy tailed distributions. Approaching this problem by modelling returns through mixture distributions, we derive robust and relative robust methodologies and discuss conic optimization approaches to solving these models.
  • Mathematical Finance Internal Seminar
14 February 2013
13:00
Marek Musiela
Abstract
The second order sensitivity of a trading position, the so called gamma, has a very real and intuitive meaning to the traders. People think that convex payoffs must generate convex prices. Being long or short of gamma is a strategy used to balance risks in options books. While the simples models, like Black Scholes, are consistent with this intuition other popular models used in the industry are not. I will give examples of simple and popular models which do not always convert a convex payoff into a convex price. I will also give the necessary and sufficient conditions under which the convexity is propagated.
  • Mathematical Finance Internal Seminar
7 February 2013
13:00
Vladimir Cherny
Abstract
We consider a problem of maximising lifetime utility of consumption subject to a drawdown constraint on undiscounted wealth process. This problem was solved by Elie and Touzi in the case of zero interest rate. We apply methodology of Azema-Yor processes to connect constrained and unconstrained wealth processes, which allows us to get the results for non-zero interest rate.
  • Mathematical Finance Internal Seminar
31 January 2013
13:00
Hanqing Jin
Abstract
General Arrow-Debreu equilibrium can be determined for expected utility maximisers by explicit solutions for individual players. When the expected utilities are distorted by probability weighting functions, players cannot find explicit optimal decisions. Zhou and Xia studied the existence of equilibrium when the probability weighting functions are the same for all individual players. In this paper, we investigate the same problem but with heterogeneous probability weighting function.
  • Mathematical Finance Internal Seminar
24 January 2013
13:00
Rasmus Varneskov (Oxford Man Institute)
Abstract
This paper analyzes a generalized class of flat-top realized kernels for estimation of the quadratic variation spectrum in the presence of a market microstructure noise component that is allowed to exhibit both endogenous and exogenous $\alpha$-mixing dependence with polynomially decaying autocovariances. In the absence of jumps, the class of flat-top estimators are shown to be consistent, asymptotically unbiased, and mixed Gaussian with the optimal rate of convergence, $n^{1/4}$. Exact bounds on lower order terms are obtained using maximal inequalities and these are used to derive a conservative MSE-optimal flat-top shrinkage. In a theoretical and/or a numerical comparison with alternative estimators, including the realized kernel, the two-scale realized kernel, and a proposed robust pre-averaging estimator, the flat-top realized kernels are shown to have superior bias reduction properties with little or no increase in finite sample variance.
  • Mathematical Finance Internal Seminar

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