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Workshop on Financial Engineering for Actuarial Mathematics

May 4-6, 2007
University of Michigan, Ann Arbor, MI


Workshop Schedule

Main Lectures in East Hall 1360. East Hall is the Math Building.

Coffee Breaks are in the Math Atrium on the second floor of East Hall.

Michigan League is on campus, a short walk northwest from East Hall.

Friday

11:30-1:00 Registration and Coffee (Math Atrium)
1:00-2:00Moshe 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 out-of-the-money long-dated 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 take-on 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 life-cycle age phased reduction in equity. I also develop a basic model of utility-maximizing 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 if-and-when 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.
2:00-2:20 Coffee.
2:20-3:20 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 multi-asset Ito type incomplete model is used. Presentation.
3:20-3:50Gordan Zitkovic, University of Texas
Title: Horizon Independent Risk Measures
Abstract: We propose a new class of risk measures that are insensitive to the time-horizon 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.
3:50-4:10 Coffee.
4:10-5:10Sam Cox, Georgia State U.
Title: Improving VaR and Skewness of Mean-Variance 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 inter-relationships cannot be characterized only by their correlations. Along these lines, we propose an optimization-based model to substantially improve the Value-at-Risk and skewness of portfolios in the mean-variance efficient frontier. Unlike other related methods in the literature, the proposed model is very intuitive, non-iterative, 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.
5:10-5:40Katharina 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.
5:45-7:15 Reception at Math Atrium.

Saturday

8:30-9:15 Coffee and Breakfast.
9:15-10:15 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.
10:15-10:30 Coffee.
10:30-11:30 Shaun Wang, Georgia State U.
Title: Risk-adjusted Correlation and Change of Multivariate Measure
Abstract: My talk shall focus on two related topics: (1) various tail correlation measures, and risk-adjustment for correlation parameters; (2) Multivariate Exponential Tilting and Multivariate Distortions as methods for adjustment of multivariate probability distributions. Presentation. Paper.
11:30-12:30 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 option-pricing 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.
12:30-2:00 Lunch at Math Atrium
2:00-3:00 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 Saa-Requejo (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 jump-diffusion model. As a by-product of the general theory we also extend the Hansen-Jagannathan bounds for the Sharpe Ratio process to the point process setting. Presentation. Paper.
3:00-3:30Sebastian Jaimungal, University of Toronto
Title: Fourier Space Time-stepping for Option Pricing with Levy Models
Abstract: Jump-diffusion and Levy models have been widely used to partially alleviate some of the biases inherent the classical Black-Scholes-Merton model. Unfortunately, the resulting pricing problem requires solving a more difficult partial-integro 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 path-dependent options (such as Bermudan, barrier, and shout options) and options on multiple assets, and naturally extends to regime-switching Levy models. Presentation. Link to Paper.
3:30-4:00 Coffee.
4:00-5:00 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 risk-loaded premium for the insurance. I will present research on empirical estimation of risk measure values and risk measure parameters. Presentation.
5:00-5:30Vytaras 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 L-statistic" -- a notion introduced herein -- is natural and particularly convenient. Indeed, the test statistic that we explore in this paper is a nested L-statistic. We discuss large-sample 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.

Sunday

8:30-9:15 Coffee and Breakfast.
9:15-10:15 Andrew Cairns, Heriot Watt University
Title: A Multifactor Generalisation of the Olivier-Smith 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 forward-rate 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.
10:15-10:45 Coffee.
10:45-11:15Matheus 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 single-life insurance and pure-endowment 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. Equity--index contracts, on the other hand, exhibit a much richer dependence on volatility, which we explore numerically in the Heston and inverse affine models. Presentation.
11:15-12:15 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 arbitrage-free 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.

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