Covariance formulas via marginal martingw

Prenctice and Cai recently introduced and studied the function C defined as the covariance function of the two marginal counting process martingales of a pair of dependent survival times (T₁, T₂ ). They show that the function C together with the marginal distributions determines the joint survival function F of (T₁, T₂ ). In this note we show how the key characterizing equation of Prentice and Cai yields a formula for the covariance of T₁ and T₂ in termsof the marginal mean residual life functions and C. The resulting formula generalizes a formula for the variance of a one-dimensional random variable Tdueto Pyke (1965). We also explore several generalizations of the covariance formula, and obtain a valid k-dimensional version of the Prentice and Cai formula.     

Bridging the gap between a stationary point process and its Palm distribution

In the context of stationary point processes measurements are usually made from a time point chosen at random or from an occurrence chosen at random. That is, either the stationary distribution P or its Palm distribution P° is the ruling probability measure. In this paper an approach is presented to bridge the gap between these distributions. We consider probability measures which give exactly the same events zero probability as P°, having simple relations with P . Relations between P and P° are derived with these intermediate measures as bridges. With the resulting Radon-Nikodym densities several well-known results can be proved easily. New results are derived. As a corollary of cross ergodic theorems a conditional version of the well-known inversion formula is proved. Several approximations of P° are considered, for instance the local characterization of P^o as a limit of conditional probability measures P° N The total variation distance between P° and P₁ can be expressed in terms of the P-distribution function of the forward recurrence time.     

The Revenue Consequences of Using Formula Apportionment to Calculate U.S. and Foreign-Source Income: A Firm-Level Analysis

This paper examines the 1989–1993 publicly available financial reports of 46 U.S.-based multinationals to estimate the revenue implications of implementing a U.S. federal formula apportionment system. Ignoring behavioral responses, we estimate shifting to an equal-weighted, three-factor formula would have increased their U.S. tax liabilities by 38 percent, with an 81 percent increase for oil and gas firms. We find the firms report a lower percentage of their worldwide profits as American profits than their American share of assets, sales, or payroll. The results may be attributed to more profitable foreign operations, tax-motivated income shifting, or measurement error.     

东北某铁路小流域水文计算与流量验证

水文计算是铁路勘察设计中的重要内容。本文针对长西铁路小流域水文计算,对地方经验公式法、铁三院法计算结果进行综合分析,并用形态法进行验证,确定适合本地区小流域流量的计算公式,为准确计算暴雨径流提供科学依据。     

Regime switching rough Heston model

This model combines two important stylized features of volatility, the rough behavior consistent with a Hurst parameter less than , and the regime switching property consistent with more long-term economic considerations. It is nevertheless highly tractable in the sense of semianalytic formulae for European options, and permits a partial Monte Carlo method of similar computational speed as the semianalytic formula (at an appropriate number of Monte Carlo simulations). While option prices are relatively insensitive to the choice of Hurst parameter, introducing rough volatility allows for a better fit to the at-the-money skew.     

Some general results for moments in bivariate distributions

The purpose of this paper is to present a closed formula to compute the moments of a general function from the knowledge of its bivariate survival function. The result is derived by utilizing an integration by parts formula for two variables, which is not readily available in the literature. Many of the existing results are obtained as special cases. Finally, two examples are presented to illustrate the results. In both the examples, mixed moments as well as moments for the series system and parallel system are obtained. The integration by parts formula in two variables, derived here, is of interest in its own right and we hope that it will be useful in other investigations. The integration by parts formula in two variables is derived as a special case of a general formula in n variables.     

Target volatility option pricing in the lognormal fractional SABR model

We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula of Itô's calculus yields an approximation formula for the price of a target volatility option in small time by the technique of freezing the coefficient. A decomposition formula in terms of Malliavin derivatives is also provided. Alternatively, we also derive closed form expressions for a small volatility of volatility expansion of the price of a target volatility option. Numerical experiments show the accuracy of the approximations over a reasonably wide range of parameters.     

实物期权在投资决策中的运用

本文通过引入实物期权的思想为投资决策评价,运用布莱克—舒尔斯和二叉树期权定价模型,给战略投资隐含的实物期权定价,使用蒙特卡罗方法来消除关键因素的不确定带来的影响。     

A Closed Form Formula for Valuing Mortgages

We develop a closed form formula for the value of a fixed-rate residential mortgage that includes the provision that the borrower can prepay at any time with no penalty. The value of the mortgage equals the expectation, under the risk neutral probability measure, of the future cash flows. We model future cash flows by estimating an empirical model of prepayment behavior. A second change of measure leads to a closed form expression for the expectation. The closed form values explain most of the time series variation in MBS prices. The closed form formula significantly shortens the time to calculate mortgage values and durations and can be a useful tool for portfolio management and hedging.     

THE SEARCH FOR A PROPORTIONATE CARE LAW BY FORMULA FUNDING IN THE ENGLISH NHS

Although the National Health Service was created to achieve equity of access to health care in 1948, over twenty years later an 'inverse care law' was seen to operate. The 1976  Report of the Resource Allocation Working Party  laid the principles of formula funding to achieve an equitable distribution of resources, to move, over time, towards the operation of a proportionate care law. These principles have been applied ever since in England. This paper describes the context, governance and subsequent development of formulas and three persistent problems: accounting for populations, their needs and variations in the unavoidable costs of providers. The paper concludes by outlining continuing problems from the past and new challenges of formula funding in England to reduce 'avoidable' inequalities in health.