Strategic Firm Behavior Under Average-Revenue-Lagged Regulation

Price caps have been shown to have incentive properties superior to traditional rate of return regulation. Average-revenue-lagged regulation (ARL) is attractive in that steady-state prices are known to be efficient. We show that the ARL scheme can be manipulated by the firm so as to yield the unregulated global profit maximum. While tests exist that can provide the regulator with evidence of this strategic behavior, we also demonstrate that the unregulated global profit maximum will not be attainable if Laspeyres (L) regulation is employed.Jel classification: L43, L51I would like to thank Michael Crew and an anonymous referee for their extremely helpful suggestions.     

Politically stable pay-as-you-go pension systems: When the social-insurance budget is too small in a democracy

The essay analyzes in an overlapping-generations model, to which extent a pay-as-you-go pension system will be the outcome of majority voting, given specific institutional set-ups. Clearly, the vote of an active person depends on his expectations about how the present decision (i.e., his contribution) is linked to the future (i.e., his benefits), when he will be retired. In the paper we employ the assumption of a basic social contract where each active voter's future benefits are positively related to his contributions. It is shown that in this framework a steady-state with a positive (though lower than optimal) level of the pension system exists, even if a new majority decision about the system takes place every period.     

中国金融控股集团发展：分业还是混业？

中国的金融控股集团可界定为跨业经营,再加上金融企业资产的弱专用性,因此现有金融管理体制下存在金融控股集团发展的空间。但本文分析认为金融控股集团的经营前景不能确定,应积极、审慎地发展。     

Replicating portfolio approach to capital calculation

The replicating portfolio (RP) approach to the calculation of capital for life insurance portfolios is an industry standard. The RP is obtained from projecting the terminal loss of discounted asset–liability cash flows on a set of factors generated by a family of financial instruments that can be efficiently simulated. We provide the mathematical foundations and a novel dynamic and path-dependent RP approach for real-world and risk-neutral sampling. We show that our RP approach yields asymptotically consistent capital estimators if the chaotic representation property holds. We illustrate the tractability of the RP approach by three numerical examples.     

An expansion in the model space in the context of utility maximization

In the framework of an incomplete financial market where the stock price dynamics are modeled by a continuous semimartingale (not necessarily Markovian), an explicit second-order expansion formula for the power investor’s value function—seen as a function of the underlying market price of risk process—is provided. This allows us to provide first-order approximations of the optimal primal and dual controls. Two specific calibrated numerical examples illustrating the accuracy of the method are also given.     

A risk-neutral equilibrium leading to uncertain volatility pricing

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.     

Chebyshev interpolation for parametric option pricing

Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real time. We concentrate on parametric option pricing (POP) as a generic instance of parametric conditional expectations and show that polynomial interpolation in the parameter space promises to considerably reduce run-times while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify broadly applicable criteria for (sub)exponential convergence and explicit error bounds. The method is most promising when the computation of the prices is most challenging. We therefore investigate its combination with Monte Carlo simulation and analyze the effect of (stochastic) approximations of the interpolation. For a wide and important range of problems, the Chebyshev method turns out to be more efficient than parametric multilevel Monte Carlo. We conclude with a numerical efficiency study.     

Explosion in the quasi-Gaussian HJM model

We study the explosion of the solutions of the SDE in the quasi-Gaussian HJM model with a CEV-type volatility. The quasi-Gaussian HJM models are a popular approach for modeling the dynamics of the yield curve. This is due to their low-dimensional Markovian representation which simplifies their numerical implementation and simulation. We show rigorously that the short rate in these models explodes in finite time with positive probability, under certain assumptions for the model parameters, and that the explosion occurs in finite time with probability one under some stronger assumptions. We discuss the implications of these results for the pricing of the zero coupon bonds and Eurodollar futures under this model.     

Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations

The aim of this paper is threefold. Firstly, we study stochastic evolution equations (with the linear part of the drift being a generator of a \(C_{0}\)-semigroup) driven by an infinite-dimensional cylindrical Wiener process. In particular, we prove, under some sufficient conditions on the coefficients, the existence and uniqueness of solutions for these stochastic evolution equations in a class of Banach spaces satisfying the so-called \(H\)-condition. Moreover, we analyse the Markov property of the solutions.Secondly, we apply the abstract results obtained in the first part to prove the existence and uniqueness of solutions to the Heath–Jarrow–Morton–Musiela (HJMM) equations in weighted Lebesgue and Sobolev spaces.Finally, we study the ergodic properties of the solutions to the HJMM equations. In particular, we find a sufficient condition for the existence and uniqueness of invariant measures for the Markov semigroup associated to the HJMM equations (when the coefficients are time-independent) in the weighted Lebesgue spaces.Our paper is a modest contribution to the theory of financial models in which the short rate can be undefined.