Optimal Changes of Gaussian Measures, with Application to Finance

We derive optimality conditions and calculate approximate solutions to the problem of determining the optimal speed of mean reversion to be applied to a Gaussian state variable. The optimality criterion is the minimization of the variance of the Radon-Nikodym derivative of the measure ”with mean-reversion ” with respect to the measure ”without mean-reversion ”under constraints. Our results have two main applications. First, we show that we can increase the speed of performing resimulation and sensitivity analysis in a Monte Carlo simulation. Second, we show that there is some phase delay between the optimal speed of mean-reversion and volatility. Incorporating this effect into preference modelling could contribute to solve the equity premium puzzle in finance.Equity premium puzzle; Monte Carlo simulation; change of measure

A Double-Sided Multiunit Combinatorial Auction for Substitutes: Theory and Algorithms

Combinatorial exchanges have existed for a long time in securities markets. In these auctions buyers and sellers can place orders on combinations, or bundles of different securities. These orders are conjunctive: they are matched only if the full bundle is available. On business-to-business (B2B) exchanges, buyers have the choice to receive the same product with different attributes; for instance the same product can be produced by different sellers. A buyer indicates his preference by submitting a disjunctive order, where he specifies how much of the product he wants, and how much he values each attribute. Only the goods with the best attributes and prices will be matched. This article considers a doubled-sided multi-unit combinatorial auction for substitutes, that is, a uniform price auction where buyers and sellers place both types of orders, conjunctive and disjunctive. We prove the existence of a linear price which is both competitive and surplus-maximizing when goods are perfectly divisible, and nearly so otherwise. We describe an algorithm to clear the market, which is particularly efficient when the number of traders is large.Combinatorial auction, economic equilibrium

Credit Risk in a Network Economy

We develop a structural model of credit risk in a network economy. In particular, we are able to account for complex counterparty relationships,where one company may be indirectly affected by the credit risk of another company in the network. In this re-spect,we generalize Jarrow and Yu (2001)and Collin-Dufresne,Goldstein and Hugonnier (2003),but do so in the rich context of a structural form model. We provide closed form formulae for the price of risky debt and equity,which depend upon the lending/borrowing relationships in the economy. Our model applies to completely general lender/borrower relationships,including looping relationships. Our formulae can apply to cases where not only ?nancial ?ows but also operations are dependent across ?rms. In order to achieve these results,we use queueing theory. This paper thus represents one of the ?rst applications of queueing theory to ?nance.Credit Risk; Capital Structure; Queueing Networks

Fractional Hida Malliavin Derivatives and Series Representations of Fractional Conditional Expectations

We represent fractional conditional expectations of a functional of fractional Brownian motion as a convergent series in L^2 space. When the target random variable is some function of a discrete trajectory of fractional Brownian motion, we obtain a backward Taylor series representation; when the target functional is generated by a continuous fractional filtration, the series representation is obtained by applying a "frozen path" operator and an exponential operator to the functional. Three examples are provided to show that our representation gives useful series expansions of ordinary expectations of target random variables

Alien Registration- Schellhorn, Henry J. (Portland, Cumberland County)

https://digitalmaine.com/alien_docs/31267/thumbnail.jp

Generating Random Vectors Using Transformation with Multiple Roots and its Applications

An approach is proposed to generate random vectors using transformation with multiple roots. This approach generalizes the one-dimensional inverse transformation with multiple roots method to higher dimensions, i.e., to random vectors with or without densities. In this approach, multiple roots of the transformation and probabilities of selecting each of the roots are derived. The strategies for constructing such a transformation are discussed and several examples are presented to motivate this simulation approach