Evaluation of insurance products with guarantee in incomplete markets

Life insurance products are usually equipped with minimum guarantee and bonus provision options. The pricing of such claims is of vital importance for the insurance industry. Risk management, strategic asset allocation, and product design depend on the correct evaluation of the written options. Also regulators are interested in such issues since they have to be aware of the possible scenarios that the overall industry will face. Pricing techniques based on the Black & Scholes paradigm are often used, however, the hypotheses underneath this model are rarely met.To overcome Black & Scholes limitations, we develop a stochastic programming model to determine the fair price of the minimum guarantee and bonus provision options. We show that such a model covers the most relevant sources of incompleteness accounted in the financial and insurance literature. We provide extensive empirical analyses to highlight the effect of incompleteness on the fair value of the option, and show how the whole framework can be used as a valuable normative tool for insurance companies and regulators.     

Differential Inclusions and Monotonicity Conditions for Nonsmooth Lyapunov Functions

In this paper we address the problem of characterizing the infinitesimal properties of functions which are nonincreasing along all the trajectories of a differential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous differential inclusions. Moreover, we show that the same criterion applies also in the case of Lipschitz continuous functions and continuous differential inclusions.     

Finite speed of propagation and local boundary conditions for wave equations with point interactions

We show that the boundary conditions entering in the definition of the self-adjoint operator describing the Laplacian plus a finite number of point interactions are local if and only if the corresponding wave equation has finite speed of propagation.

     

Efficient similarity factorization of rank-1 modifications

For the solution of stiff ODEs by implicit methods one has to solve sequences of algebraic systems, whose Jacobian is the identity minus a multiple of the 'system' Jacobian of the right hand side. The latter can be successively approximated by a new 'two-sided rank-1' formula yielding only a moderate increase in the number of iterations compared to Newton's method. However, so far we have only been able to achieve the reduction in the linear algebra effort per integration step from O (n 3) to O (n 2) as long as the size is kept constant. To obtain an effort of O (n 2) seems to require an update of a similarity reduction of the system Jacobian to Hessenberg form or even a band matrix. As we have found no O (n 2) algorithms for updating such factorizations in literature, we discuss an idea to approximate the update with enough accuracy to ensure rapid convergence of the underlying implicit equation solver. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Feasible Operations and Applicative Theories Based on λη

We study a theory PTO(λη) of polynomial time computability on the type of binary strings (in the style of [6]), as embedded in full lambda calculus with total application and extensionality. We prove that the closed terms of (provable) type W → W are exactly the polynomial time operations. This answers a conjecture of Strahm [13].     

Projective representations i. projective lines over rings

We discuss representations of the projective line over a ringR with 1 in a projective space over some (not necessarily commutative) fieldK. Such a representation is based upon a (K, R)-bimoduleU. The points of the projective line overR are represented by certain subspaces of the projective space ℙ(K, U ×U) that are isomorphic to one of their complements. In particular, distant points go over to complementary subspaces, but in certain cases, also non-distant points may have complementary images.     

Robust clustering around regression lines with high density regions

Robust methods are needed to fit regression lines when outliers are present. In a clustering framework, outliers can be extreme observations, high leverage points, but also data points which lie among the groups. Outliers are also of paramount importance in the analysis of international trade data, which motivate our work, because they may provide information about anomalies like fraudulent transactions. In this paper we show that robust techniques can fail when a large proportion of non-contaminated observations fall in a small region, which is a likely occurrence in many international trade data sets. In such instances, the effect of a high-density region is so strong that it can override the benefits of trimming and other robust devices. We propose to solve the problem by sampling a much smaller subset of observations which preserves the cluster structure and retains the main outliers of the original data set. This goal is achieved by defining the retention probability of each point as an inverse function of the estimated density function for the whole data set. We motivate our proposal as a thinning operation on a point pattern generated by different components. We then apply robust clustering methods to the thinned data set for the purposes of classification and outlier detection. We show the advantages of our method both in empirical applications to international trade examples and through a simulation study.     

Penalty variable sample size method for solving optimization problems with equality constraints in a form of mathematical expectation

Numerical Algorithms - Equality-constrained optimization problems with deterministic objective function and constraints in the form of mathematical expectation are considered. The constraints are...     

The swap graph of the finite soluble groups

A graph is reflexive if the second largest eigenvalue of its adjacency matrix is less than or equal to 2. In this paper, we characterize trees whose line graphs are reflexive. It turns out that these trees can be of arbitrary order—they can have either a unique vertex of arbitrary degree or pendant paths of arbitrary lengths, or both. Since the reflexive line graphs are Salem graphs, we also relate some of our results to the Salem (graph) numbers.     

Objective bayesian analysis of the Yule–Simon distribution with applications

The Yule–Simon distribution is usually employed in the analysis of frequency data. As the Bayesian literature, so far, has ignored this distribution, here we show the derivation of two objective priors for the parameter of the Yule–Simon distribution. In particular, we discuss the Jeffreys prior and a loss-based prior, which has recently appeared in the literature. We illustrate the performance of the derived priors through a simulation study and the analysis of real datasets.