Spyridon D. Vrontos

DESIGN OF OPTIMAL BONUS-MALUS SYSTEMS WITH A FREQUENCY AND A SEVERITY COMPONENT ON AN INDIVIDUAL BASIS IN AUTOMOBILE INSURANCE

The majority of optimal Bonus-Malus Systems (BMS) presented up to now in the actuarial literature assign to each policyholder a premium based on the number of his accidents. In this way a policyholder who had an accident with a small size of loss is penalized unfairly in the same way with a policyholder who had an accident with a big size of loss. Motivated by this, we develop in this paper, the design of optimal BMS with both a frequency and a severity component. The optimal BMS designed are based both on the number of accidents of each policyholder and on the size of loss (severity) for each accident incurred. Optimality is obtained by minimizing the insurer’s risk. Furthermore we incorporate in the above design of optimal BMS the important a priori information we have for each policyholder. Thus we propose a generalised BMS that takes into consideration simultaneously the individual’s characteristics, the number of his accidents and the exact level of severity for each accident.

A Quantile Regression Approach to Equity Premium Prediction

We propose a quantile regression approach to equity premium forecasting. Robust point forecasts are generated by both fixed and time-varying weighting schemes, thus exploiting the entire distributional information associated with each predictor. Further gains are achieved by incorporating the forecast combination methodology in our quantile regression setting. Our approach using a time-varying weighting scheme delivers statistically and economically significant out-of-sample forecasts relative to the historical average benchmark and the combined mean predictive regression modeling approach.

On a renewal risk process with dependence under a Farlie - Gumbel - Morgenstern copula

In this article, we consider an extension to the renewal or Sparre Andersen risk process by introducing a dependence structure between the claim sizes and the interclaim times through a Farlie–Gumbel–Morgenstern copula proposed by Cossette et al. (2010) for the classical compound Poisson risk model. We consider that the inter-arrival times follow the Erlang(n) distribution. By studying the roots of the generalised Lundberg equation, the Laplace transform (LT) of the expected discounted penalty function is derived and a detailed analysis of the Gerber–Shiu function is given when the initial surplus is zero. It is proved that this function satisfies a defective renewal equation and its solution is given through the compound geometric tail representation of the LT of the time to ruin. Explicit expressions for the discounted joint and marginal distribution functions of the surplus prior to the time of ruin and the deficit at the time of ruin are derived. Finally, for exponential claim sizes explicit expressions and numerical examples for the ruin probability and the LT of the time to ruin are given.

Out-of-Sample Equity Premium Prediction: A Complete Subset Quantile Regression Approach

This paper extends the complete subset linear regression framework to a quantile regression setting. We employ complete subset combinations of quantile forecasts in order to construct robust and accurate equity premium predictions. Our recursive algorithm that selects, in real time, the best complete subset for each predictive regression quantile succeeds in identifying the best subset in a time- and quantile-varying manner. We show that our approach delivers statistically and economically signi cant out-of-sample forecasts relative to both the historical average benchmark and the complete subset mean regression approach.

Performance evaluation of mutual fund investments: the impact of non-normality and time-varying volatility

Extending previous work on mutual fund pricing, this paper introduces the idea of modeling the conditional distribution of mutual fund returns using a fat tailed density and a time-varying conditional variance. This approach takes into account the stylized facts of mutual fund return series, that is heteroscedasticity and deviations from normality. We evaluate mutual fund performance using multifactor asset pricing models, with the relevant risk factors being identified through standard model selection techniques. We explore potential impacts of our approach by analyzing individual mutual funds and show that it can be economically important.

Ruin probability at a given time for a model with liabilities of the fractional Brownian motion type: A partial differential equation approach

In this paper we study the ruin probability at a given time for liabilities of diffusion type, driven by fractional Brownian motion with Hurst exponent in the range (0.5, 1). Using fractional Itô calculus we derive a partial differential equation the solution of which provides the ruin probability. An analytical solution is found for this equation and the results obtained by this approach are compared with the results obtained by Monte-Carlo simulation.

Quantile Forecast Combinations in Realised Volatility Prediction

This paper tests whether it is possible to improve point, quantile and density forecasts of realised volatility by conditioning on a set of predictive variables. We employ quantile autoregressive models augmented with macroeconomic and financial variables. Complete subset combinations of both linear and quantile forecasts enable us to efficiently summarise the information content in the candidate predictors. Our findings suggest that no single variable is able to provide more information for the evolution of the volatility distribution beyond that contained in its own past. The best performing variable is the return on the stock market followed by the inflation rate. Our complete subset approach achieves superior point, quantile and density predictive performance relative to the univariate models and the autoregressive benchmark.