Pricing Excess-of-loss Reinsurance Contracts Against Catastrophic Loss

This paper develops a pricing methodology and pricing estimates for the proposed Federal excess-of- loss (XOL) catastrophe reinsurance contracts. The contracts, proposed by the Clinton Administration, would provide per-occurrence excess-of-loss reinsurance coverage to private insurers and reinsurers, where both the coverage layer and the fixed payout of the contract are based on insurance industry losses, not company losses. In financial terms, the Federal government would be selling earthquake and hurricane catastrophe call options to the insurance industry to cover catastrophic losses in a loss layer above that currently available in the private reinsurance market. The contracts would be sold annually at auction, with a reservation price designed to avoid a government subsidy and ensure that the program would be self supporting in expected value. If a loss were to occur that resulted in payouts in excess of the premiums collected under the policies, the Federal government would use its ability to borrow at the risk-free rate to fund the losses. During periods when the accumulated premiums paid into the program exceed the losses paid, the buyers of the contracts implicitly would be lending money to the Treasury, reducing the costs of government debt. The expected interest on these "loans" offsets the expected financing (borrowing) costs of the program as long as the contracts are priced appropriately. By accessing the Federal government's superior ability to diversify risk inter-temporally, the contracts could be sold at a rate lower than would be required in conventional reinsurance markets, which would potentially require a high cost of capital due to the possibility that a major catastrophe could bankrupt some reinsurers. By pricing the contacts at least to break even, the program would provide for eventual private-market "crowding out" through catastrophe derivatives and other innovative catastrophic risk financing mechanisms. We develop prices for the contracts using two samples of catastrophe losses: (1) historical catastrophic loss experience over the period 1949-1994 as reported by Property Claim Services; and (2) simulated catastrophe losses based on an engineering simulation analysis conducted by Risk Management Solutions. We used maximum likelihood estimation techniques to fit frequency and severity probability distributions to the catastrophic loss data, and then used the distributions to estimate expected losses under the contracts. The reservation price would be determined by adding an administrative expense charge and a risk premium to the expected losses for the specified layer of coverage. We estimate the expected loss component of the government's reservation price for proposed XOL contracts covering the entire U.S., California, Florida, and the Southeast. We used a loss layer of $25-50 billion for illustrative purposes.

Lie Superalgebras and the Multiplet Structure of the Genetic Code II: Branching Schemes

Continuing our attempt to explain the degeneracy of the genetic code using basic classical Lie superalgebras, we present the branching schemes for the typical codon representations (typical 64-dimensional irreducible representations) of basic classical Lie superalgebras and find three schemes that do reproduce the degeneracies of the standard code, based on the orthosymplectic algebra osp(5|2) and differing only in details of the symmetry breaking pattern during the last step.Comment: 34 pages, 9 tables, LaTe

Generating-function method for fusion rules

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion article. Although the Kac-Walton algorithm provides a method for constructing a fusion generating function from the corresponding tensor-product generating function, we describe a more powerful approach which starts by first defining the set of fusion elementary couplings from a natural extension of the set of tensor-product elementary couplings. A set of inequalities involving the level are derived from this set using Farkas' lemma. These inequalities, taken in conjunction with the inequalities defining the tensor products, define what we call the fusion basis. Given this basis, the machinery of our previous paper may be applied to construct the fusion generating function. New generating functions for sp(4) and su(4), together with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy

An Empirical Analysis of the Economic Impact of Federal Terrorism Reinsurance

This paper examines the role of the federal government in the market for terrorism reinsurance. We investigate the stock price response of affected industries to a sequence of thirteen events culminating in the enactment of the Terrorism Risk Insurance Act (TRIA) of 2002. In the industries most likely to be affected by TRIA banking, construction, insurance, real estate investment trusts, transportation, and public utilities the stock price effect was primarily negative. The Act was at best value-neutral for property-casualty insurers because it eliminated the option not to offer terrorism insurance. The negative response of the other industries may be attributable to the Act's impeding more efficient private market solutions, failing to address nuclear, chemical, and biological hazards, and reducing market expectations of federal assistance following future terrorist attacks.

Securitized Risk Instruments as Alternative Pension Fund Investments

Recent years have seen the introduction of a new class of derivative securities based on exotic underlyings such as natural catastrophes and weather. This paper analyzes the pros and cons of these new securities as assets for institutional investors. It is argued that the underlyings on which these derivatives trade have very low correlations with other factors that move the investment markets, potentially enabling investors to shift the efficient investment frontier in a favorable direction. However, there in very little data on the effects on the market of a large natural catastrophe, and these securities may be especially susceptible to liquidity problems and credit risk. The paper explores these issues in more detail, as well as providing information on the actual and optimal design of such contracts

Volunteering and well-being : do self-esteem, optimism, and perceived control mediate the relationship?

Volunteers play a vital role in modern societies by boosting the labor force within both the public and private sectors. While the factors that may lead people to volunteer have been investigated in a number of studies, the means by which volunteering contributes to the well-being of such volunteers is poorly understood. It has been suggested through studies that focus on the absence of depression in volunteers that self-esteem and sense of control may be major determinants of the increased well-being reported by volunteers. This is consistent with the homeostatic model of subjective well-being, which proposes that self-esteem, optimism, and perceived control act as buffers that mediate the relationship between environmental experience and subjective well-being (SWB). Using personal well-being as a more positive measure of well-being than absence of depression, this study further explored the possible mediating role of self-esteem, optimism, and perceived control in the relationship between volunteer status and well-being. Participants (N = 1,219) completed a 97-item survey as part of the Australian Unity Wellbeing project. Variables measured included personal well-being, self-esteem, optimism, and a number of personality and psychological adjustment factors. Analyses revealed that perceived control and optimism, but not self-esteem, mediated the relationship between volunteer status and personal well-being.<br /

Managerial decision making under uncertainty: the case of Twenty20 cricket

We consider managerial decision making by examining the impact of decisions taken by cricket captains on Twenty20 International (T20I) match outcomes. In particular, we examine whether pressure from external commentators is associated with suboptimal decision making by captains. Using data from over 300 T20I matches, we find little evidence that either winning the toss or choosing to bat first improves the likelihood of winning. Despite this, we find that captains in T20I cricket are significantly more likely to choose to bat rather than bowl after winning the toss, a finding that is consistent with social pressure constraining captains’ decision making

Equivalent qubit dynamics under classical and quantum noise

We study the dynamics of quantum systems under classical and quantum noise, focusing on decoherence in qubit systems. Classical noise is described by a random process leading to a stochastic temporal evolution of a closed quantum system, whereas quantum noise originates from the coupling of the microscopic quantum system to its macroscopic environment. We derive deterministic master equations describing the average evolution of the quantum system under classical continuous-time Markovian noise and two sets of master equations under quantum noise. Strikingly, these three equations of motion are shown to be equivalent in the case of classical random telegraph noise and proper quantum environments. Hence fully quantum-mechanical models within the Born approximation can be mapped to a quantum system under classical noise. Furthermore, we apply the derived equations together with pulse optimization techniques to achieve high-fidelity one-qubit operations under random telegraph noise, and hence fight decoherence in these systems of great practical interest.Comment: 5 pages, 2 figures; converted to PRA format, added Fig. 2, corrected typo

A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength

We demonstrate how using two-qubit composite rotations a high fidelity controlled-NOT (CNOT) gate can be constructed, even when the strength of the interaction between qubits is not accurately known. We focus on the exchange interaction oscillation in silicon based solid-state architectures with a Heisenberg Hamiltonian. This method easily applies to a general two-qubit Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity when a single application of the composite rotations is combined with a modest level of Hamiltonian characterisation. Operating the robust CNOT gate in a suitably characterised system means concatenation of the composite pulse is unnecessary, hence reducing operation time, and ensuring the gate operates below the threshold required for fault-tolerant quantum computation.Comment: 9 pages, 8 figure

Generating-function method for tensor products

This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp's character method. An alternative approach to the construction of tensor-product generating functions is then presented which overcomes most of the technical difficulties associated with the character method. It is based on the reformulation of the problem of calculating tensor products in terms of the solution of a set of linear and homogeneous Diophantine equations whose elementary solutions represent ``elementary couplings''. Grobner bases provide a tool for generating the complete set of relations between elementary couplings and, most importantly, as an algorithm for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced version of hep-th/9811113 (with new title); to appear in J. Math. Phy