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.

Bond markets where prices are driven by a general marked point process

We investigate the term structure for the case when interest rates are allowed to be driven by a general marked point process as well as by a Wiener process. Developing a theory which allows for measure-valued trading portfolios we study existence and uniqueness of a martingale measure, as well as completeness of the bond market. We also give sufficient conditions for the existence of an affine term structure. Developing the appropriate forward measures we give formulas for interest rate derivatives.Term structure of interest rates; arbitrage; bond markets; interest rates; martingales; jump processes; completeness; affine term structure

Agent Causation: Before and After the Ontological Turn

Imagine Ludwig has a cup of tea for breakfast. He\ud pours it; he eats his egg until it seems to him that the tea\ud should have the right temperature; he moves his hand to\ud the cup, puts his fingers at the handle, and then, careful\ud not to spill anything, he does something with his arm;\ud namely, he raises it, and if all goes well he then drinks the\ud tea without burning his lips.\ud The rising of Ludwig"s arm surely has a cause. But\ud what is the cause? Defenders of agent causation, such as\ud Thomas Reid (1788), Richard Taylor (1966), Roderick\ud Chisholm (1976a), and many more recent authors (see\ud Swinburne 1997, ch. 5; Thorp 1980; Meixner 1999; Clarke\ud 1996; O'Connor 2000) have argued that the rising of\ud Ludwig"s arm is caused by Ludwig himself. Some events\ud are caused, not by other events, but by concrete things, by\ud substances, more specifically by intentional agents

A benchmark approach to filtering in finance

The paper propsoed the use of the growth optimal portfolio for pricing and hedging in imcomplete markets when there are unobserved factors that have to be filtered. The proposed filtering framework is applicable also in cases when there does not exist an equivalent risk neutral martingale measure. The reduction of the variance of derivative prices for increasing degrees of available iformation is measured

Partially Observable Control Problems with Compulsory Shifts of the State

Stochastic control problems with partial state observation and the long-run average cost criterion are among the most difficult dynamic stochastic optimization problems and almost nothing has so far appeared in the literature concerning their solution. On the other hand many problems in Engineering, Operations Research, and the Economic and Social Sciences can be modelled as problems of the above type. In the present paper we study conditions under which the filtering process associated with the partially observed state process has a unique invariant measure and describe ways to approximate it. We finally discuss the applications of these results to the construction of nearly optimal controls

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

Combined Filtering and Parameter Estimation for Discrete-Time Systems Driven by Approximately White Gaussian Noise Disturbances

In the problem of combined filtering and parameter estimation one considers a stochastic dynamical system whose state x_t is only partially observed through an observation process y_t. The stochastic model for the process pair (x_t, y_t) depends furthermore on an unknown parameter theta. Given an observation history of the process y_t, the problem then consists in estimating recursively both the current state x_t of the system (filtering) as well as the value theta of the parameter (Bayesian parameter estimation). The problem is a rather difficult one: Even if, conditionally on a given value of theta, the process pair (x_t, y_t) satisfies a linear-Gaussian model so that the filtering problem for x_t can be solved via the familiar Kalman-Bucy filter; when theta is unknown, the problem becomes a difficult nonlinear filtering problem. The present paper, partly based on previous joint work of one of the authors, makes a contribution towards the solution of this problem in the case of discrete time and of a (conditionally on theta) linear model for x_t, y_t. The solution that is obtained is shown to be robust with respect to small variations in the a priori distributions in the model, in particular those of the disturbances