A Hull and White formula for a general stochastic volatility jump-diffusion model with applications to the study of the short-time behavior of the implied volatility

In this paper, generalizing results in Alòs, León and Vives (2007b), we see that the dependence of jumps in the volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use Malliavin calculus techniques for Lévy processes based on Løkka (2004), Petrou (2006), and Solé, Utzet and Vives (2007).

Mixed equilibrium in a Downsian model with a favored candidate

This paper examines competition in the standard one-dimensional Downsian model of two-candidate elections, but where one candidate (A) enjoys an advantage over the other candidate (D). Voters' preferences are Euclidean, but any voter will vote for candidate A over candidate D unless D is closer to her ideal point by some fixed distance \delta. The location of the median voter's ideal point is uncertain, and its distribution is commonly known by both candidates. The candidates simultaneously choose locations to maximize the probability of victory. Pure strategy equilibria often fails to exist in this model, except under special conditions about \delta and the distribution of the median ideal point. We solve for the essentially unique symmetric mixed equilibrium, show that candidate A adopts more moderate policies than candidate D, and obtain some comparative statics results about the probability of victory and the expected distance between the two candidates' policies.

A simple model of multiple equilibria based on risk

This paper shows how risk may aggravate fluctuations in economies with imperfect insurance and multiple assets. A two period job matching model is studied, in which risk averse agents act both as workers and as entrepreneurs. They choose between two types of investment: one type is riskless, while the other is a risky activity that creates jobs.Equilibrium is unique under full insurance. If investment is fully insured but unemployment risk is uninsured, then precautionary saving behavior dampens output fluctuations. However, if both investment and employment are uninsured, then an increase in unemployment gives agents an incentive to shift investment away from the risky asset, further increasing unemployment. This positive feedback may lead to multiple Pareto ranked equilibria. An overlapping generations version of the model may exhibit poverty traps or persistent multiplicity. Greater insurance is doubly beneficial in this context since it can both prevent multiplicity and promote risky investment.

A two-mean reverting-factor model of the term structure of interest rates

This paper presents a two--factor model of the term structure ofinterest rates. We assume that default free discount bond prices aredetermined by the time to maturity and two factors, the long--term interestrate and the spread (difference between the long--term rate and theshort--term (instantaneous) riskless rate). Assuming that both factorsfollow a joint Ornstein--Uhlenbeck process, a general bond pricing equationis derived. We obtain a closed--form expression for bond prices andexamine its implications for the term structure of interest rates. We alsoderive a closed--form solution for interest rate derivatives prices. Thisexpression is applied to price European options on discount bonds andmore complex types of options. Finally, empirical evidence of the model'sperformance is presented.

A BPE model for the Burgers' equation

We study the BPE (Brownian particle equation) model of the Burgers equationpresented in the preceeding article [6]. More precisely, we are interestedin establishing the existence and uniqueness properties of solutions usingprobabilistic techniques.

The variability of money velocity in a generalized cash-in-advance model

This paper presents a general equilibrium model of money demand wherethe velocity of money changes in response to endogenous fluctuations in the interest rate. The parameter space can be divided into two subsets: one where velocity is constant and equal to one as in cash-in-advance models, and another one where velocity fluctuates as in Baumol (1952). Despite its simplicity, in terms of paramaters to calibrate, the model performs surprisingly well. In particular, it approximates the variability of money velocity observed in the U.S. for the post-war period. The model is then used to analyze the welfare costs of inflation under uncertainty. This application calculates the errors derived from computing the costs of inflation with deterministic models. It turns out that the size of this difference is small, at least for the levels of uncertainty estimated for the U.S. economy.

A model of market-making

The two essential features of a decentralized economy taken intoaccount are, first, that individual agents need some informationabout other agents in order to meet potential trading partners,which requires some communication or interaction between theseagents, and second, that in general agents will face tradinguncertainty. We consider trade in a homogeneous commodity. Firmsdecide upon their effective supplies, and may create their ownmarkets by sending information signals communicating theirwillingness to sell. Meeting of potential trading partners isarranged in the form of shopping by consumers. The questions to beconsidered are: How do firms compete in such markets? And what arethe properties of an equilibrium? We establish existenceconditions for a symmetric Nash equilibrium in the firms'strategies, and analyze its characteristics. The developedframework appears to lend itself well to study many typicalphenomena of decentralized economies, such as the emergence ofcentral markets, the role of middlemen, and price-making.

A finite-population revenue management model and a risk-ratio procedure for the joint estimation of population size and parameters

Many dynamic revenue management models divide the sale period into a finite number of periods T and assume, invoking a fine-enough grid of time, that each period sees at most one booking request. These Poisson-type assumptions restrict the variability of the demand in the model, but researchers and practitioners were willing to overlook this for the benefit of tractability of the models. In this paper, we criticize this model from another angle. Estimating the discrete finite-period model poses problems of indeterminacy and non-robustness: Arbitrarily fixing T leads to arbitrary control values and on the other hand estimating T from data adds an additional layer of indeterminacy. To counter this, we first propose an alternate finite-population model that avoids this problem of fixing T and allows a wider range of demand distributions, while retaining the useful marginal-value properties of the finite-period model. The finite-population model still requires jointly estimating market size and the parameters of the customer purchase model without observing no-purchases. Estimation of market-size when no-purchases are unobservable has rarely been attempted in the marketing or revenue management literature. Indeed, we point out that it is akin to the classical statistical problem of estimating the parameters of a binomial distribution with unknown population size and success probability, and hence likely to be challenging. However, when the purchase probabilities are given by a functional form such as a multinomial-logit model, we propose an estimation heuristic that exploits the specification of the functional form, the variety of the offer sets in a typical RM setting, and qualitative knowledge of arrival rates. Finally we perform simulations to show that the estimator is very promising in obtaining unbiased estimates of population size and the model parameters.

Surviving in a competitive spatial market: The threshold capture model

Most facility location decision models ignore the fact that for a facility to survive it needs a minimum demand level to cover costs. In this paper we present a decision model for a firm thatwishes to enter a spatial market where there are several competitors already located. This market is such that for each outlet there is a demand threshold level that has to be achievedin order to survive. The firm wishes to know where to locate itsoutlets so as to maximize its market share taking into account the threshold level. It may happen that due to this new entrance, some competitors will not be able to meet the threshold and therefore will disappear. A formulation is presented together with a heuristic solution method and computational experience.

A model of collateral, investment and adverse selection

This paper characterizes the relationship between entrepreneurial wealth and aggregate investmentunder adverse selection. Its main finding is that such a relationship need not bemonotonic. In particular, three results emerge from the analysis: (i) pooling equilibria, in whichinvestment is independent of entrepreneurial wealth, are more likely to arise when entrepreneurialwealth is relatively low; (ii) separating equilibria, in which investment is increasing inentrepreneurial wealth, are most likely to arise when entrepreneurial wealth is relatively highand; (iii) for a given interest rate, an increase in entrepreneurial wealth may generate a discontinuousfall in investment.

Model selection and error estimation

We study model selection strategies based on penalized empirical loss minimization. We point out a tight relationship between error estimation and data-based complexity penalization: any good error estimate may be converted into a data-based penalty function and the performance of the estimate is governed by the quality of the error estimate. We consider several penalty functions, involving error estimates on independent test data, empirical {\sc vc} dimension, empirical {\sc vc} entropy, andmargin-based quantities. We also consider the maximal difference between the error on the first half of the training data and the second half, and the expected maximal discrepancy, a closely related capacity estimate that can be calculated by Monte Carlo integration. Maximal discrepancy penalty functions are appealing for pattern classification problems, since their computation is equivalent to empirical risk minimization over the training data with some labels flipped.

A recoverable production planning model

Aware of the importance of developing new alternatives to improve the performance of the companies, our purpose in this paper is to develop a medium term production planning model that deals with the concepts of Partnership and Reverse Logistics. Our model takes advantage of the synergies of integration, developing a model for global production planning that generates the optimal production and purchasing schedule for all the companies integrating a logistic chain. In a second part of the paper we incorporate products returns to the first model proposed, and analyze the implications they have over this model. We use some examples with different configurations of supply chains varying the number of production plants, distribution centers and recovery plants. To solve the model we have combined optimization and simulation procedures.

A model of conglomeration and synergy traps

We present a model of conglomeration motivated by technology synergies and strategic reductions in variable costs in the face of competitive pressures. The resulting firm integration is neither horizontal nor vertical but rather congeneric integration of firms in related industries. We endogenize the industrial conglomeration structure and examine the effects of competition between conglomerates, and between a conglomerate and independent firms. We show that there is an equilibrium synergy trap in which conglomerates are formed to exploit economies of scope, but resulting profits are lower than under the status quo. We also show that strategic firm integration can occur even in the presence of diseconomies of scope. The model helps to explain features of recent mergers and acquisitions experience.

Change of individual BMI in Switzerland and the USA: a multilevel model for growth

Objective The aim is to analyze and compare individual BMI growth patterns of adults from Switzerland and the U.S. Methods The analyses are based on data from two population representative longitudinal household surveys, one from Switzerland, the other from the U.S. Each data set contains up to four data points for each adult individual. We use multilevel models for growth. Results It can be shown that growth patterns are different in different cohorts in the two countries: there are only small growth differences in the youngest and oldest, but large differences in the middle ages. The individual BMI increase of the middle age Swiss amounts to only half of that in the comparable U.S. individuals. Conclusion Given the much higher BMI level especially in the youngest cohort, this points to severe obesity problems in the U.S. middle aged population in the near future. A positive correlation between individual BMI level and growth may aggravate this fact.

Analyses of six homologous proteins of Protochlamydia amoebophila UWE25 encoded by large GC-rich genes (lgr): a model of evolution and concatenation of leucine-rich repeats.

BACKGROUND: Along the chromosome of the obligate intracellular bacteria Protochlamydia amoebophila UWE25, we recently described a genomic island Pam100G. It contains a tra unit likely involved in conjugative DNA transfer and lgrE, a 5.6-kb gene similar to five others of P. amoebophila: lgrA to lgrD, lgrF. We describe here the structure, regulation and evolution of these proteins termed LGRs since encoded by "Large G+C-Rich" genes. RESULTS: No homologs to the whole protein sequence of LGRs were found in other organisms. Phylogenetic analyses suggest that serial duplications producing the six LGRs occurred relatively recently and nucleotide usage analyses show that lgrB, lgrE and lgrF were relocated on the chromosome. The C-terminal part of LGRs is homologous to Leucine-Rich Repeats domains (LRRs). Defined by a cumulative alignment score, the 5 to 18 concatenated octacosapeptidic (28-meric) LRRs of LGRs present all a predicted alpha-helix conformation. Their closest homologs are the 28-residue RI-like LRRs of mammalian NODs and the 24-meres of some Ralstonia and Legionella proteins. Interestingly, lgrE, which is present on Pam100G like the tra operon, exhibits Pfam domains related to DNA metabolism. CONCLUSION: Comparison of the LRRs, enable us to propose a parsimonious evolutionary scenario of these domains driven by adjacent concatenations of LRRs. Our model established on bacterial LRRs can be challenged in eucaryotic proteins carrying less conserved LRRs, such as NOD proteins and Toll-like receptors.