Robust Equilibria in Indefinite Linear-Quadratic Differential Games

Equilibria in dynamic games are formulated often under the assumption that the players have full knowledge of the dynamics to which they are subject. Here, we formulate equilibria in which players are looking for robustness and take model uncertainty explicitly into account in their decisions. Specifically, we consider feedback Nash equilibria in indefinite linear-quadratic differential games on an infinite time horizon. Model uncertainty is represented by a malevolent input which is subject to a cost penalty or to a direct bound. We derive conditions for the existence of robust equilibria in terms of solutions of sets of algebraic Riccati equations.     

Treasury Management Model with Foreign Exchange Exposure

In this paper we formulate a model for foreign exchange exposure management and (international) cash management taking into consideration random fluctuations of exchange rates. A vector error correction model (VECM) is used to predict the random behaviour of the forward as well as spot rates connecting dollar and sterling. A two-stage stochastic programming (TWOSP) decision model is formulated using these random parameter values. This model computes currency hedging strategies, which provide rolling decisions of how much forward contracts should be bought and how much should be liquidated.The model decisions are investigated through ex post simulation and backtesting in which value at risk (VaR) for alternative decisions are computed. The investigation (a) shows that there is a considerable improvement to “spot only” strategy, (b) provides insight into how these decisions are made and (c) also validates the performance of this model.     

A note on generalized nonlinear diagonal dominance

In this paper, an open problem, proposed by A. Frommer, about nonlinear generalized diagonal dominance, is solved on some weak restriction, a counterexample is presented if such a restriction is omitted, and some new properties of nonlinear generalized diagonally dominant functions are investigated.     

Nanotechnology and the need for risk governance

After identifying the main characteristics and prospects of nanotechnology as an emerging technology, the paper presents the general risks associated with nanotechnology applications and the deficits of the risk governance process today, concluding with recommendations to governments, industry, international organizations and other stakeholders. The International Risk Governance Council (IRGC) has identified a governance gap between the requirements pertaining to the nano- rather than the micro-/macro- technologies. The novel attributes of nanotechnology demand different routes for risk-benefit assessment and risk management, and at present, nanotechnology innovation proceeds ahead of the policy and regulatory environment. In the shorter term, the governance gap is significant for those passive nanostructures that are currently in production and have high exposure rates; and is especially significant for the several ‘active’ nanoscale structures and nanosystems that we can expect to be on the market in the near future. Active nanoscale structures and nanosystems have the potential to affect not only human health and the environment but also aspects of social lifestyle, human identity and cultural values. The main recommendations of the report deal with selected higher risk nanotechnology applications, short- and long-term issues, and global models for nanotechnology governance.     

Government-provided annuities under insolvency risk

This paper seeks to determine whether governments should intervene in the private annuity market by directly providing public insurance in the form of annuities when both the government and the insurance companies could default. It is found that, although the government could default, intervening by means of an annuity can improve social welfare if the insurance companies could default and the expected return on the public annuity is greater than the rate of return on a risk-free bond. We also find that, under actuarially fair pricing, the government should provide more in terms of a public annuity than the optimal amount of the annuity that the individual purchases in the private market if the government is less likely to default on the public annuity than an insurance company would in the case of a private annuity.     

Bayesian parameter inference for models of the Black and Scholes type

In this paper, we describe a general method for constructing the posterior distribution of the mean and volatility of the return of an asset satisfying dS=SdX for some simple models of X. Our framework takes as inputs the prior distributions of the parameters of the stochastic process followed by the underlying, as well as the likelihood function implied by the observed price history for the underlying. As an application of our framework, we compute the value at risk (VaR) and conditional VaR (CVaR) measures for the changes in the price of an option implied by the posterior distribution of the volatility of the underlying. The implied VaR and CVaR are more conservative than their classical counterpart, since it takes into account the estimation risk that arises due to parameter uncertainty. Copyright © 2008 John Wiley & Sons, Ltd.     

Risk theory insight into a zone-adaptive control strategy

The main purpose of this paper is a risk theory insight into the problem of asset-liability and solvency adaptive management. In the multiperiodic insurance risk model composed of chained classical risk models, a zone-adaptive control strategy, essentially similar to that applied in Directives [Directive 2002/13/EC of the European Parliament and of the Council of 5 March 2002, Brussels, 5 March 2002], is introduced and its performance is examined analytically. That examination was initiated in [Malinovskii, V.K., 2006b. Adaptive control strategies and dependence of finite time ruin on the premium loading. Insurance: Math. Econ. (in press)] and is based on the application of the explicit expression for the finite-time ruin probability in the classical risk model. The result of independent interest in the paper is the representation of that finite-time ruin probability in terms of asymptotic series, as time increases.     

带干扰的多险种Cox风险模型的破产概率

考虑到保险公司在实际经营中收益所具有的不确定性和风险经营的多元化,建立了一个更现实的风险模型即带干扰的多险种Cox风险模型.运用鞅论得到了该模型最终破产概率的上界,并对Lundberg不等式作了推广.     

A note on taxation,incentives and risk sharing

The necessary and sufficient conditions for a tax system to guarantee the consistency of private and public evaluation of risky projects are derived. A stochastic dominance approach is used.     

Simplest cases of nth-degree stochastic dominance

Le p(n) be the fewest number of support points for probability distributions p and q for which p stochastically dominates q of degree n but not of any degrees less than n. Then ?(n) = n + 1 for n = 1,2,3, and ?(n) = 4 for all larger n.