Ruin probabilities in a finite-horizon risk model with investment and reinsurance

A finite horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Obtaining explicit optimal solutions for the minimizing ruin probability problem is a difficult task. Therefore, we consider an alternative method commonly used in ruin theory, which consists in deriving inequalities that can be used to obtain upper bounds for the ruin probabilities and then choose the control to minimize the bound. We finally specialize our results to the particular, but relevant, case of exponentially distributed claims and compare for this case our bounds with the classical Lundberg bound.Risk process, Reinsurance and investment, Lundberg’s inequality, 91B30, 93E20, 60J28

On Filtering in Markovian Term Structure Models (An Approximation Approach)

We study a nonlinear filtering problem to estimate, on the basis of noisy observations of forward rates, the market price of interest rate risk as well as the parameters in a particular term structure model within the Heath-Jarrow-Morton family. An approximation approach is described for the actual computation of the filter.filter approximations; Heath-Jarrow-Morton model; market price interest rate risk; markovian representations; measure transformation; nonlinear filtering; term structure of interest rates

Estimation in Models of the Instantaneous Short Term Interest Rate By Use of a Dynamic Bayesian Algorithm

This paper considers the estimation in models of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we set up the stochastic dynamics for the discretely compounded market observed rates and propose a dynamic Bayesian estimation algorithm (i.e. a filtering algorithm) for a time-discretised version of the resulting interest rate dynamics. The filter solution is computed via a further spatial discretization (quantization) and the convergence of the latter to its continuous counterpart is discussed in detail. The method is applied to simulated data and is found to give a reasonable estimate of the conditional density function and to be not too demanding computationally.

Ruin probabilities in a finite-horizon risk model with investment and reinsurance

A finite horizon insurance model is studied where the risk/reserve process can be controlled by reinsurance and investment in the financial market. Obtaining explicit optimal solutions for the minimizing ruin probability problem is a difficult task. Therefore, we consider an alternative method commonly used in ruin theory, which consists in deriving inequalities that can be used to obtain upper bounds for the ruin probabilities and then choose the control to minimize the bound. We finally specialize our results to the particular, but relevant, case of exponentially distributed claims and compare for this case our bounds with the classical Lundberg bound

A Benchmark Approach to Filtering in Finance

The paper proposes the use of the growth optimal portfolio for the construction of financial market models with unobserved factors that have to be filtered. This benchmark approach avoids any measure transformation for the pricing of derivatives. The suggested framework allows to measure the reduction of the variance of derivative prices for increasing degrees of available information.financial modelling; filter methods; benchmark approach; growth optimal portfolio

On the Separation of Estimation and Control in Risk-Sensitive Investment Problems under Incomplete Observation

A typical approach to tackle stochastic control problems with partial observation is to separate the control and estimation tasks. However, it is well known that this separation generally fails to deliver an actual optimal solution for risk-sensitive control problems. This paper investigates the separability of a general class of risk-sensitive investment management problems when a finite-dimensional filter exists. We show that the corresponding separated problem, where instead of the unobserved quantities, one considers their conditional filter distribution given the observations, is strictly equivalent to the original control problem. We widen the applicability of the so-called Modified Zakai Equation (MZE) for the study of the separated problem and prove that the MZE simplifies to a PDE in our approach. Furthermore, we derive criteria for separability. We do not solve the separated control problem but note that the existence of a finite-dimensional filter leads to a finite state space for the separated problem. Hence, the difficulty is equivalent to solving a complete observation risk-sensitive problem. Our results have implications for existing risk-sensitive investment management models with partial observations in that they establish their separability. Their implications for future research on new applications is mainly to provide conditions to ensure separability

The Volatility of the Instantaneous Spot Interest Rate Implied by Arbitrage Pricing - A Dynamic Bayesian Approach

This paper considers the estimation of the volatility of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we derive a relationship between observed LIBOR rates and certain unobserved instantaneous forward rates. We determine the stochastic dynamics for these rates under the risk- neutral measure and propose a filtering estimation algorithm for a time- discretised version of the resulting interest rate dynamics based on dynamic Bayesian updating. The method is applied to US Treasury rates of various maturities and is found to give a reasonable model fit.

Large portfolio losses: A dynamic contagion model

Using particle system methodologies we study the propagation of financial distress in a network of firms facing credit risk. We investigate the phenomenon of a credit crisis and quantify the losses that a bank may suffer in a large credit portfolio. Applying a large deviation principle we compute the limiting distributions of the system and determine the time evolution of the credit quality indicators of the firms, deriving moreover the dynamics of a global financial health indicator. We finally describe a suitable version of the "Central Limit Theorem" useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis.Comment: Published in at http://dx.doi.org/10.1214/08-AAP544 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Benchmark Approach to Portfolio Optimization under Partial Information

This paper proposes a filtering methodology for portfolio optimization when some factors of the underlying model are only partially observed. The level of information is given by the observed quantities that are here supposed to be the primary securities and empirical log-price covariations. For a given level of information we determine the growth optimal portfolio, identify locally optimal portfolios that are located on a corresponding Markowitz efficient frontier and present an approach for expected utility maximization. We also present an expected utility indifference pricing approach under partial information for the pricing of nonreplicable contracts. This results in a real world pricing formula under partial information that turns out to be independent of the subjective utility of the investor and for which an equivalent risk neutral probability measure need not exist.portfolio ptimization; partial information; filtering, growth optimal portfolio; expected utility maximization; utility indifference pricing; real world pricing formula