SCIENTIFIC PROGRAMS AND ACTIVITIES

April 20, 2014

Actuarial Science and Mathematical Finance Group Meetings
2007-08

at the Fields Institute

The Actuarial Science and Mathematical Finance research group meets on a regular basis to discuss various problems and methods that arise in Finance and Actuarial Science. These informal meetings are held at the Fields Institute for Mathematical Sciences and are open to the public. Talks range from original research to reviews of classical papers and overviews of new and interesting mathematical and statistical techniques/frameworks that arise in the context of Finance and Actuarial Science.

Meetings are normally held on Wednesdays from 2pm to 3:30pm, but check calendar for exceptions.
If you are interested in presenting in this series please contact the seminar organizer: Prof. Sebastian Jaimungal (sebastian [dot] jaimungal [at] utoronto [dot] ca).

May 26, 2008
Wednesday
2:00 p.m

Speaker: Roger Lee, Department of Mathematics, University of Chicago
Implied Volatility in Relation to Realized Volatility
If realized volatility is a nonrandom constant, then of course the Black-Scholes implied volatility equals that constant realized volatility. If realized volatility is random, then how does it relate to implied volatility? We answer this question with respect to several notions of implied volatility -- the Black-Scholes definition, and two model-free definitions. We start by assuming only the positivity and continuity of the underlying price paths.

Based on joint work with Peter Carr.

May 21, 2008
Wednesday
2:00 p.m

Hans J.H.Tuenter, Energy Markets, Ontario Power Generation
Expected Overshoot in the Case of Normal Variables with Positive Mean
The expected overshoot in the case of normal variables with positive mean is studied, and simpler self-contained derivations of the known results are given. We also give new series expansions with better convergence properties. Applications in finance are found in option pricing, where overshoot corrections have been used in the pricing of discrete barrier options.

May 7, 2008
Wednesday
2:00 p.m
Andrei Badescu, Department of Statistics, University of Toronto
Return Probabilities of Stochastic Fluid Flows and Their Use in Collective Risk Theory
One way of analyzing insurance risk models is by making use of the existing connections with stochastic fluid flows. Matrix-analytic methods constitute a useful approach to the study of such fluid flow models. In the present talk we illustrate the derivation of several first passage probabilities whose numerical calculation is very tractable, based on the structure and the probabilistic meaning of certain matrices describing these fluid models. In the end, we enumerate several classes of risk processes that can be analyzed using these probabilistic tools.
Feb 5, 2008
Tuesday
2:00 p.m
Speaker: Matheus Grasselli, Department of Mathematics, Mc Master University.
Indifference pricing of insurance contracts: stochastic volatility and stochastic interest rates

In the first part of this talk I will present an asymptotic expansion for the indifference price of equity-linked insurance contracts in when the underlying financial asset follows a 2-factor stochastic volatility model with fast mean reversion. For the second part of the talk, I consider path-dependent contracts under stochastic interest rates, obtain optimal investment strategies using stocks and bonds, and present integral representations for the price of contracts that depend exclusively on the paths of interest rates.

Jan 23, 2008
Wednesday
2:00 p.m
Speaker: Sebastian Jaimungal, University of Toronto
Indifference Valuation for Credit Default Swaps through a Structural Approach

Traditional structural models assume that firm value is a tradable security and proceed to value defaultable bonds as European or Barrier options on firm value. We introduce a model in which default is driven by a visible (but not tradable) credit worthiness index (CWI) that is correlated to the firm's equity value. Default occurs when the CWI falls below a critical level at which time equity drops to zero. Given the incomplete nature of this market setting, we adopt stochastic optimal control methods through utility indifference to extract the implied bond values and CDS spreads.

[ joint work with Georg Sigloch ]

Nov 30, 2007
Friday
2:00 p.m.
Speaker: Erhan Bayraktar, Department of Mathematics, University of Michigan.
Pricing Asian Options for Jump Diffusions

In this talk, I will discuss the pricing problem for the European Asian options in jump diffusion models. Following the method I used to solve the problem for American options, a sequence of functions are also constructed to approximate the price of Asian options. However, because the pay-off functions are not necessarily bounded, new methods are introduced to prove the regularity of functions in this sequence. As a result, this sequence of functions converge unformly and exponentially fast to the price of Asian option on compact sets. This provides us a fast numerical algorithm. At the end of this talk, I will present the numerical performance of this algorithm for Merton's model and Kou's model.

Joint work with Hao Xing.
Relevant papers are available at: http://arxiv.org/abs/0707.2432,m http://arxiv.org/abs/math.OC/0703782

Nov 7, 2007
Wednesday
2:00 p.m

Speaker: Marcel Rindisbacher, Rotman Business School, University of Toronto

Dynamic Asset-Liability Management for Defined-Benefit Pension Plans
A dynamic asset-liability management model for defined-benefit pension plans is developed. The plan sponsor exhibits features of loss aversion and tolerance for limited shortfalls in assets under management relative to the liability due. The optimal contribution policy, the optimal dividend policy and the associated asset allocation rule are derived and analyzed. Sound Asset-Liability Management is shown to entail withdrawals as well as contributions from the pension fund.

Oct. 31, 2007
Wednesday
2:00 p.m

Speaker: Marcel Rindisbacher, Rotman Business School, University of Toronto

Monte Carlo Methods for Optimal Portfolios
This talk provides an introduction and short overview on some recent Monte Carlo Methods to solve optimal dynamic asset allocation problems. Using the martingale approach and elements from Malliavin calculus, a fully
probabilistic representation of the optimal portfolio policy is derived. This representation is of the Feynman-Kac type and therefore key to formulateMonte Carlo methods. The Malliavin method is compared with alternative Monte

Carlo techniques that do not rely on an exact probabilistic representation. Finally, the Malliavin Monte Carlo method is illustrated with several examples.

Oct. 3,2007
Wednesday
2:00 p.m

Speaker: Michael Walker, Department of Physics, University of Toronto

Calibration, the Timing of Defaults, and the Marking to Market of CDO's
The talk begins with a qualitative description of CDO's and their usefulness in helping banks to shed the default risk of a loan portfolio. Then the iTraxx and CDO markets for CDO's are described. For these markets, there are a large number of market prices for CDO contracts of different maturities and different tranches established for a given underlying portfolio on a given day. The problem of calibrating a model to this large number of market prices has been one of the central problems of CDO research, and the loss surface approach to calibration is described.

The impact of calibration across maturities on the determination of the timing of defaults is discussed, as is the impact of the timing of defaults on the marking to market of CDO contracts. In so far as time permits, an introduction to the extension of the loss surface model to a dynamic model, capable of being calibrated to dynamics-sensitive contracts such as options on CDO's and leveraged super-senior tranches, will be given.

Sept. 14, 2007
Friday

Speaker: Michael Ludkovski,
Dept Mathemtics, University of Michigan

Relative Hedging of Systematic Mortality Risk
I will first review recent models of stochastic mortality and the associated problems in pricing mortality contingent claims under stochastic mortality age structures. The focus of my talk will then be on capturing the internal population-level cross-hedge between components of an insurer's portfolio, especially between life annuities and life insurance. I will derive and compare several linear mechanisms which value claims under various martingale measures, and then pass to exhaustive analysis of the exponential premium principle which is the representative nonlinear pricing rule in this framework. The results will be illustrated with a couple of numerical examples that show the relative importance of model parameters. Based on joint work with Erhan Bayraktar and Jenny Young (U of Michigan).