Power Utility Maximization in Constrained Exponential L\'evy Models

We study power utility maximization for exponential L\'evy models with portfolio constraints, where utility is obtained from consumption and/or terminal wealth. For convex constraints, an explicit solution in terms of the L\'evy triplet is constructed under minimal assumptions by solving the Bellman equation. We use a novel transformation of the model to avoid technical conditions. The consequences for q-optimal martingale measures are discussed as well as extensions to non-convex constraints.Comment: 22 pages; forthcoming in 'Mathematical Finance

Copulas in finance and insurance

Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

Copulas in finance and insurance

Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing.Dependence structure, Extremal values, Copula modeling, Copula review

Estimation of Expected Returns, Time Consistency of A Stock Return Model, and Their Application to Portfolio Selection

Longer horizon returns are modeled by two approaches, which have different impact on skewness and excess kurtosis. The Levy approach, which considers the random variable at longer horizon as the cumulants of i.i.d random variables from shorter horizons, tends to decrease skewness and excess kurtosis in a faster rate along the time horizon than the real data implies. On the other side, the scaling approach keeps skewness and excess kurtosis constant along the time horizon. The combination of these two approaches may have a better performance than each one of them. This empirical work employs the mixed approach to study the returns at five time scales, from one-hour to two-week. At all time scales, the mixed model outperforms the other two in terms of the KS test and numerous statistical distances. Traditionally, the expected return is estimated from the historical data through the classic asset pricing models and their variations. However, because the realized returns are so volatile, it requires decades or even longer time period of data to attain relatively accurate estimates. Furthermore, it is questionable to extrapolate the expected return from the historical data because the return is determined by future uncertainty. Therefore, instead of using the historical data, the expected return should be estimated from data representing future uncertainty, such as the option prices which are used in our method. A numeraire portfolio links the option prices to the expected return by its striking feature, which states that any contingent claim's price, if denominated by this portfolio, is the conditional expectation of its denominated future payoffs under the physical measure. It contains the information of the expected return. Therefore, in this study, the expected returns are estimated from the option calibration through the numeraire portfolio pricing method. The results are compared to the realized returns through a linear regression model, which shows that the difference of the two returns is indifferent to the major risk factors. This demonstrates that the numeraire portfolio pricing method provides a good estimator for the expected return. The modern portfolio theory is well developed. However, various aspects are questioned in the implementation, e.g., the expected return is not properly estimated using historical data, the return distribution is assumed to be Gaussian, which does not reflect the empirical facts. The results from the first two studies can be applied to this problem. The constructed portfolio using this estimated expected return is superior to the reference portfolios with expected return estimated from historical data. Furthermore, this portfolio also outperforms the market index, SPX

Why VAR Fails: Long Memory and Extreme Events in Financial Markets

The Value-at-Risk (VAR) measure is based on only the second moment of a rates of return distribution. It is an insufficient risk performance measure, since it ignores both the higher moments of the pricing distributions, like skewness and kurtosis, and all the fractional moments resulting from the long - term dependencies (long memory) of dynamic market pricing. Not coincidentally, the VaR methodology also devotes insufficient attention to the truly extreme financial events, i.e., those events that are catastrophic and that are clustering because of this long memory. Since the usual stationarity and i.i.d. assumptions of classical asset returns theory are not satisfied in reality, more attention should be paid to the measurement of the degree of dependence to determine the true risks to which any investment portfolio is exposed: the return distributions are time-varying and skewness and kurtosis occur and change over time. Conventional mean-variance diversification does not apply when the tails of the return distributions ate too fat, i.e., when many more than normal extreme events occur. Regrettably, also, Extreme Value Theory is empirically not valid, because it is based on the uncorroborated i.i.d. assumption.Long memory, Value at Risk, Extreme Value Theory, Portfolio Management, Degrees of Persistence

Managing uncertainty:financial, actuarial and statistical modelling.

present value; Value; Actuarial;