
Workshop on Financial Engineering for Actuarial MathematicsMay 46, 2007

11:301:00  Registration and Coffee (Math Atrium) 
1:002:00  Moshe Milevsky, York University Title: Portfolio Choice with Puts: Evidence from Variable Annuities Abstract: I will discuss the portfolio choice and asset allocation behavior of individuals who acquire an outofthemoney longdated put option on their investment funds. Using a unique database of over half a million variable annuity (VA) policyholders provided by seven different insurance companies, I will document that these investors takeon 5% to 30% additional risky/equity exposure when this longevity put option is selected. And, when this longevity put option is not elected  so the investment portfolio resembles a conventional mutual fund  I confirm the classical lifecycle age phased reduction in equity. I also develop a basic model of utilitymaximizing behavior in the presence of this longevity put that indeed justifies the increased allocation to risk, provided the investor is willing, able and understands to exercise the annuity option ifandwhen it matures in the money. This work is the first to examine actual asset allocations within variable annuity policies, which is currently a $1.5 trillion dollar market in the U.S. and is expected to grow as aging baby boomers take control of their own retirement assets. Presentation. 
2:002:20  Coffee. 
2:203:20  Thaleia Zariphopoulou, University of Texas Title: Investment performance measurement, risk tolerance and optimal portfolio choice Abstract: A new approach to measure the dynamic performance of investment strategies is introduced. To this aim, a family of stochastic processes defined on [0,\infty) and indexed by a wealth argument is used. Optimality is associated with their martingale property along the optimal wealth trajectory. The optimal portfolios are constructed via stochastic feedback controls that are functionally related to differential constraints of fast diffusion type. A multiasset Ito type incomplete model is used. Presentation. 
3:203:50  Gordan Zitkovic, University of Texas Title: Horizon Independent Risk Measures Abstract: We propose a new class of risk measures that are insensitive to the timehorizon at which the realization of the risk takes place. These measures arise naturally when the investment horizon is unspecified, or when the investor is looking for trading strategies that perform well independently of the choice of the measurement (normalization) point. We give several examples of such measures, characterize them in the entropic case and relate them to the notion of a forward utility of Musiela and Zariphopoulou. This is joint work with Thaleia Zariphopoulou. Presentation. 
3:504:10  Coffee. 
4:105:10  Sam Cox, Georgia State U. Title: Improving VaR and Skewness of MeanVariance Portfolios Abstract: In recent years, there has been a growing interest in developing methodologies to take into account moments of higher order than the variance, in the context of optimal risk reward portfolio allocation. This is due to the widely accepted belief that asset returns and insurance product line margins are not normally distributed, and their interrelationships cannot be characterized only by their correlations. Along these lines, we propose an optimizationbased model to substantially improve the ValueatRisk and skewness of portfolios in the meanvariance efficient frontier. Unlike other related methods in the literature, the proposed model is very intuitive, noniterative, simple to implement, and it can be readily and efficiently solved with state of the art optimization solvers. These characteristics should make our methodology very appealing to both practitioners and researchers in portfolio and risk management. To illustrate the characteristics of the model we present comprehensive numerical experiments. Paper. 
5:105:40  Katharina Zaglauer, University of Wisconsin Milwaukee Title: Risk Neutral Valuation of Participating Life Insurance Contracts in a Stochastic Interest Rate Environment Abstract: We present a framework in which participating life insurance contracts including predominant kinds of guarantees and options can be valued and analyzed in a stochastic interest rate environment. In particular, the different option elements can be priced and analyzed separately. We use Monte Carlo and discretization methods to derive the respective values. The sensitivity of the contract and guarantee values with respect to multiple parameters is studied using the bonus distribution schemes as introduced in Bauer et al. (2006). This is joint work with Bauer (Ulm, Germany). Presentation. Paper. 
5:457:15  Reception at Math Atrium. 
8:309:15  Coffee and Breakfast. 
9:1510:15  Mary Hardy, University of Waterloo Title: Valuation and Funding for Defined Benefit Minimum Guarantee Pension Plans Abstract: The Defined Benefit (DB) underpin hybrid pension plan offers an attractive combination of benefit security and upside potential for pension plan members, and cost containment for employers. In this paper the DB underpin guarantee is valued as a financial option, within the traditional funding paradigms of actuarial science. Contribution rates are developed for stylized funding methods based on the principles of Entry Age Normal, Projected Unit Credit and Traditional Unit Credit funding. Presentation. 
10:1510:30  Coffee. 
10:3011:30  Shaun Wang, Georgia State U. Title: Riskadjusted Correlation and Change of Multivariate Measure Abstract: My talk shall focus on two related topics: (1) various tail correlation measures, and riskadjustment for correlation parameters; (2) Multivariate Exponential Tilting and Multivariate Distortions as methods for adjustment of multivariate probability distributions. Presentation. Paper. 
11:3012:30  Elias Shiu, University of Iowa Title: Dynamic Fund Protection Abstract: Nowadays, many products sold by life insurance companies are basically mutual funds, wrapped around with some insurance features or guarantees. These guarantees are financial options that should be priced, hedged, and reserved using modern optionpricing theory, with mathematical tools such as martingales, Brownian motion, stochastic differential equations, and so on. This talk will explain "dynamic fund protection" and show how it is priced. Presentation. 
12:302:00  Lunch at Math Atrium 
2:003:00  Tomas Bjork, Stockholm School of Economics Title: Towards a general theory of good deal bounds Abstract: We consider an incomplete market in the form of a multidimensional Markovian factor model, driven by a general marked point process (representing discrete jump events) as well as by a standard multidimensional Wiener process. Within this framework we study arbitrage free good deal pricing bounds for derivative assets along the lines of Cochrane and SaaRequejo (2000), extending these results to the point process case, while at the same time obtaining a radical simplification of the theory. As a concrete application we present numerical results for the classic Merton jumpdiffusion model. As a byproduct of the general theory we also extend the HansenJagannathan bounds for the Sharpe Ratio process to the point process setting. Presentation. Paper. 
3:003:30  Sebastian Jaimungal, University of Toronto Title: Fourier Space Timestepping for Option Pricing with Levy Models Abstract: Jumpdiffusion and Levy models have been widely used to partially alleviate some of the biases inherent the classical BlackScholesMerton model. Unfortunately, the resulting pricing problem requires solving a more difficult partialintegro differential equation (PIDE) and although several approaches for solving the PIDE have been suggested in the literature, none are entirely satisfactory. All treat the integral and diffusive terms asymmetrically, truncate large jumps and are difficult to extend to higher dimensions. We present a new efficient algorithm, based on transform methods, which symmetrically treats the diffusive and integrals terms, is applicable to a wide class of pathdependent options (such as Bermudan, barrier, and shout options) and options on multiple assets, and naturally extends to regimeswitching Levy models. Presentation. Link to Paper. 
3:304:00  Coffee. 
4:005:00  Bruce Jones, University of Western Ontario Title: Empirical estimation of risk measure values and parameters Abstract: Risk measures have attracted considerable recent interest in the actuarial and financial literature. Risk measures can be used to assign to a random outcome a value that reflects the distribution associated with the outcome. For example, if the random outcome is a loss that is covered by insurance, then a risk measure can be used to determine a riskloaded premium for the insurance. I will present research on empirical estimation of risk measure values and risk measure parameters. Presentation. 
5:005:30  Vytaras Brazauskas, University of Wisconsin, Milwaukee Title: A nonparametric test for comparing the riskiness of portfolios Abstract: Inspired by the problem of testing hypotheses about the equality of several risk measure values, we find that the "nested Lstatistic"  a notion introduced herein  is natural and particularly convenient. Indeed, the test statistic that we explore in this paper is a nested Lstatistic. We discuss largesample properties of the statistic, investigate its performance using a simulation study, and consider an example involving the comparison of risk measure values where the risks of interest are those associated with tornado damage in different time periods and different regions. In collaboration with Jones (UWO), Puri (IU), and Zitikis (UWO). Presentation. 
7:00  Conference Banquet at Michigan League. 
8:309:15  Coffee and Breakfast. 
9:1510:15  Andrew Cairns, Heriot Watt University Title: A Multifactor Generalisation of the OlivierSmith Model for Stochastic Mortality Abstract: Recent years have seen the development of a number of models for the future development of aggregate mortality rates. Amongst these the Olivier and Smith model (Olivier and Jeffery, 2004, Olivier and Smith, 2005) was developed within the forwardrate framework discussed by Cairns et al. (2006) and Miltersen and Persson (2005). This model has a number of useful properties that make it a very good model for use in the valuation of life insurance contracts that incorporate embedded options. We discuss here a generalisation of the Olivier and Smith model. Dynamics of the model in its published form are driven by a sequence of univariate gamma random variables. We demonstrate that the model in this form does not adequately match historical data. We discuss a generalisation of the model that uses multivariate Gamma random variables as drivers. This approach potentially gives us much greater control over the term structure of volatility of spot survival probabilities and over the correlation term structure. Presentation. 
10:1510:45  Coffee. 
10:4511:15  Matheus Grasselli, McMaster University Title: Hedging insurance contracts using financial markets with stochastic volatility Abstract: We consider the problem of partially hedging the risk of an insurance contract by trading in a financial market. Because of the typical duration of such contracts, it is unrealistic to assume that the volatilities of the underlying financial assets are constant. Accordingly, we investigate how the results of Young and Zariphopoulou (2002) and Young (2003) can be generalized for markets with stochastic volatility. We show that stochastic volatility does not affect the indifference price of either singlelife insurance and pureendowment contracts, unless the agent uses a random horizon, in which the indifference price depends on the speed of mean reversion and long term average of the volatility, as well as the mean rate of return of the stock. Equityindex contracts, on the other hand, exhibit a much richer dependence on volatility, which we explore numerically in the Heston and inverse affine models. Presentation. 
11:1512:15  Martin Schweizer, ETH Zürich Title: Market models for option prices: Some recent developments Abstract: We consider a market in which one can liquidly trade (1) a riskless bank account, (2) a stock, and (3) a family of European call options written on that stock. How can one model this situation in an arbitragefree and tractable way? In particular, we want to ensure that calibration to observed option prices in the market is practically feasible. We show that this leads to nontrivial parametrization problems, and we explain in several situations how these can be overcome. Moreover, we prove existence and uniqueness results for classes of such dynamical models in situations with an infinite number of options. This is joint work with Johannes Wissel (ETH Zurich). Presentation. 