Modelling dynamic portfolio risk using risk drivers of elliptical processes

The situation of a limited availability of historical data is frequently encountered in portfolio risk estimation, especially in credit risk estimation. This makes it difficult, for example, to find statistically significant temporal structures in the data on the single asset level. By contrast, there is often a broader availability of cross-sectional data, i.e. a large number of assets in the portfolio. This paper proposes a stochastic dynamic model which takes this situation into account. The modelling framework is based on multivariate elliptical processes which model portfolio risk via sub-portfolio specific volatility indices called portfolio risk drivers. The dynamics of the risk drivers are modelled by multiplicative error models (MEMs)-as introduced by Engle [Engle, R.F., 2002. New frontiers for ARCH models. J. Appl. Econom. 17, 425-446]-or by traditional ARMA models. The model is calibrated to Moody’s KMV Credit Monitor asset returns (also known as firm-value returns) given on a monthly basis for 756 listed European companies at 115 time points from 1996 to 2005. This database is used by financial institutions to assess the credit quality of firms. The proposed risk drivers capture the volatility structure of asset returns in different industry sectors. A characteristic cyclical as well as a seasonal temporal structure of the risk drivers is found across all industry sectors. In addition, each risk driver exhibits idiosyncratic developments. We also identify correlations between the risk drivers and selected macroeconomic variables. These findings may improve the estimation of risk measures such as the (portfolio) Value at Risk. The proposed methods are general and can be applied to any series of multivariate asset or equity returns in finance and insurance.     

Heavy traffic limits for queues with non-stationary path-dependent arrival processes

Queueing Systems - In this paper, we develop a diffusion approximation for the transient distribution of the workload process in a standard single-server queue with a non-stationary Polya arrival...     

A multivariate stochastic model with non-stationary trend component

The purposes of this paper are to introduce a multivariate non-stationary stochastic time series model without individual detrending and to extract the multiple relationships between variables. To infer the statistical relation between variables, we attempt to estimate the co-movement of multivariate non-stationary time series components. The model is expressed in state-space form, and time series components are estimated by the maximum likelihood method using numerical optimization algorithm. The Kalman filter algorithm is used to compute the likelihood of the model. The AIC procedure gives a criterion for selecting the best model fit for the data. The multiple relationship becomes clear by analysing estimated AR coefficients. Real economic data are used for a numerical example.     

Weak convergence of non-stationary multivariate marked processes with applications to martingale testing

This paper establishes the weak convergence of a class of marked empirical processes of possibly non-stationary and/or non-ergodic multivariate time series sequences under martingale conditions. The assumptions involved are similar to those in Brown's martingale central limit theorem. In particular, no mixing conditions are imposed. As an application, we propose a test statistic for the martingale hypothesis and we derive its asymptotic null distribution. Finally, a Monte Carlo study shows that the asymptotic results provide good approximations for small and moderate sample sizes. An application to the S&P 500 is also considered.     

Modelling the brain processes of conscious states

Based on a precise definition of consciousness in terms of awareness and volition, a simple model is developed to simulate the essential activity of the conscious brain. The model is based on the concepts of cognitive science but is consistent with the known neuroanatomical structure of the primate cortex. Awareness and volition are identified with the gain and creation of information at the microscopic level in channels of the neural membrane, and a method is devised for the computer simulation of the quantum mechanical indeterminacy of these processes. A simple computer program is described and listed to simulate the cognitive processing of sensory data and the concomitant initiation and excecution of voluntary activity.     

A Factorization problem and the problem of predicting non-stationary vector-valued stochastic processes

Summary In this paper a prediction theory is developed under the general idea that the infinite dimensional covariance matrix is a self-adjoint element in a symmetric Banach algebra. The usual Wiener's spectral factorization method for solving stationary Wiener-Hopf equations has been extended to this algebra. Finally, a theorem for factoring a positive definite covariance matrix into upper and lower triangular factors with similar inverses has been proved.     

Numerical solution of a PDE model for a ratchet-cap pricing with BGM interest rate dynamics

In this paper we present a new numerical method to price an interest rate derivative. The financial product consists of a particular ratchet cap contract which contains a set of ratchet caplets. For this purpose, we first pose the PDE pricing model for each ratchet caplet by means of Feynman-Kac theorem. The underlying interest rates are the forward LIBOR rates, the dynamics of which are assumed to follow the recently introduced BGM (LMM) market model. For the set of PDEs associated to the ratchet caplets pricing problems, we propose a second order Crank-Nicolson characteristics time discretization scheme combined with a finite element discretization in the interest rate variables. In order to illustrate the performance of the numerical methods, we present an academic test and a real example of a particular ratchet cap pricing. In the second case, a comparison between the results obtained by Monte Carlo simulation and the proposed method is presented.     

Optimal policy for a dynamic,non-stationary,stochastic inventory problem with capacity commitment

This paper studies a single-product, dynamic, non-stationary, stochastic inventory problem with capacity commitment, in which a buyer purchases a fixed capacity from a supplier at the beginning of a planning horizon and the buyer’s total cumulative order quantity over the planning horizon is constrained with the capacity. The objective of the buyer is to choose the capacity at the beginning of the planning horizon and the order quantity in each period to minimize the expected total cost over the planning horizon. We characterize the structure of the minimum sum of the expected ordering, storage and shortage costs in a period and thereafter and the optimal ordering policy for a given capacity. Based on the structure, we identify conditions under which a myopic ordering policy is optimal and derive an equation for the optimal capacity commitment. We then use the optimal capacity and the myopic ordering policy to evaluate the effect of the various parameters on the minimum expected total cost over the planning horizon.     

Modelling and computing (Rn, Sn) policies for inventory systems with non-stationary stochastic demand

This paper addresses the single-item, non-stationary stochastic demand inventory control problem under the non-stationary (R, S) policy. In non-stationary (R, S) policies two sets of control parameters—the review intervals, which are not necessarily equal, and the order-up-to-levels for replenishment periods—are fixed at the beginning of the planning horizon to minimize the expected total cost. It is assumed that the total cost is comprised of fixed ordering costs and proportional direct item, inventory holding and shortage costs. With the common assumption that the actual demand per period is a normally distributed random variable about some forecast value, a certainty equivalent mixed integer linear programming model is developed for computing policy parameters. The model is obtained by means of a piecewise linear approximation to the non-linear terms in the cost function. Numerical examples are provided.     

Partitioned time stepping schemes for the non-stationary dual-fracture-matrix fluid flow model

This paper presents the coupled, and decoupled schemes for the naturally fractured reservoir consists of the triple-porosity medium. More specifically, the triple-porosity medium contains three contagious porous medium with more permeable macrofractures, less permeable microfractures, and matrix region which is often known as dual-fracture-matrix fluid flow model. Since the matrix has fluid communication with less permeable microfractures, and macrofratures are fed by the microfractures only, the global domain is divided into two subdomains by considering the traditional dual-porosity region and more permeable macrofractures region respectively. The flow and mass exchange between less permeable microfractures and more permeable macrofractures are modeled by two-fluid communication interface conditions while no-communication interface condition is imposed on between matrix and macrofractures region. The weak formulation and the well-posedness of the dual-fracture-matrix model are derived. Furthermore, coupled, implicit-explicit and data-passing partitioned schemes are proposed. The stability and the optimal convergence analysis are derived for both decoupled schemes. Five numerical examples are presented to illustrate the accuracy of the numerical methods and the applicability of the dual-fracture-matrix fluid flow model. Moreover, the parameter sensitivity analysis is performed in the fourth numerical example.     

Two-compartment model interacting with proliferating regulatory factor

In this short work, by combining the total cell evolution curve and the two-compartment model, the evolution of one of the subpopulations is simulated while the system interacts with a proliferating regulatory factor.     

A second-order decoupled algorithm with different subdomain time steps for the non-stationary Stokes/Darcy model

Numerical Algorithms - In this paper, we propose and analyze a second-order decoupled algorithm with different subdomain time steps for the non-stationary Stokes/Darcy model. It is based on the...     

The Andronov-Hopf bifurcation in a model of a hypothetical gene regulatory network

Stability of the limit cycles of small amplitude resulting from the Andronov-Hopf bifurcation is studied in a system of ordinary differential equations which describes the behavior of a hypothetical gene regulatory network.     

Modelling the profitability of credit cards by Markov decision processes

This paper derives a Markov decision process model for the profitability of credit cards, which allows lenders to find an optimal dynamic credit limit policy. The states of the system are based on the borrower’s behavioural score and the decisions are what credit limit to give the borrower each period. In determining which Markov chain best describes the borrower’s performance, second order as well as first order Markov chains are considered and estimation procedures developed that deal with the low default levels that may exist in the data. A case study is given in which the optimal credit limit is derived and the results compared with the actual outcomes.     

双复合Poisson风险模型

研究了保费收取过程是复合Po isson过程,索赔总额是复合Po isson过程的风险模型,给出了不破产概率的积分表示,以及在特殊情况下不破产概率的具体表达式,并用鞅方法得出了破产概率满足的Lundberg不等式和一般公式.     

Multidimensional Lee-Carter model with switching mortality processes

This paper proposes a multidimensional Lee-Carter model, in which the time dependent components are ruled by switching regime processes. The main feature of this model is its ability to replicate the changes of regimes observed in the mortality evolution. Changes of measure, preserving the dynamics of the mortality process under a pricing measure, are also studied. After a review of the calibration method, a 2D, 2-regimes model is fitted to the male and female French population, for the period 1946-2007. Our analysis reveals that one regime corresponds to longevity conditions observed during the decade following the second world war, while the second regime is related to longevity improvements observed during the last 30 years. To conclude, we analyze, in a numerical application, the influence of changes of measure affecting transition probabilities, on prices of life and death insurances.     

Singular perturbation analysis and gene regulatory networks with delay

The problem of how the dynamics of the smooth gene networks is related to the simplified dynamics of the Boolean networks is studied. The emphasis is put on the gene regulatory networks with delay. Asymptotic analysis which is applied in the paper goes back to Tikhonov’s theory of singular perturbed differential equations and a modified algorithm of reducing delay equations to ordinary differential equations. A number of illustrative examples complements the theory which is offered in the paper.     

Modeling gene regulatory networks with piecewise linear differential equations

Microarray chips generate large amounts of data about a cell’s state. In our work we want to analyze these data in order to describe the regulation processes within a cell. Therefore, we build a model which is capable of capturing the most relevant regulating interactions and present an approach how to calculate the parameters for the model from time-series data. This approach uses the discrete approximation method of least squares to solve a data fitting modeling problem. Furthermore, we analyze the features of our proposed system, i.e., which kinds of dynamical behaviors the system is able to show.     

A dynamic input-output model with renewable resources

The paper studies a generalisation of the dynamic Leontief input-output model. The standard dynamic Leontief model will be extended with the balance equation of renewable resources. The renewable stocks will increase regenerating and decrease exploiting primary natural resources. In this study the controllability of this extended model is examined by taking the consumption as the control parameter. Assuming balanced growth for both consumption and production, we investigate the exhaustion of renewable resources in dependence on the balanced growth rate and on the rate of natural regeneration. In doing so, classic results from control theory and on eigenvalue problems in linear algebra are applied.