A game interpretation of the Neumann problem for fully nonlinear parabolic and elliptic equations

We provide a deterministic-control-based interpretation for a broad class of fully nonlinear parabolic and elliptic PDEs with continuous Neumann boundary conditions in a smooth domain. We construct families of two-person games depending on a small parameter which extend those proposed by Kohn and Serfaty (2010). These new games treat a Neumann boundary condition by introducing some specific rules near the boundary. We show that the value function converges, in the viscosity sense, to the solution of the PDE as the parameter tends to zero. Moreover, our construction allows us to treat both the oblique and the mixed type Dirichlet-Neumann boundary conditions.Comment: 58 pages, 2 figure

Barriers and Optimal Investment

This paper analyzes the impact of different types of barriers on the decision to invest using a simple framework based on stochastic discount factors. Our intuitive approach proposes an alternative to the real options methodology that does not rely on the “smooth-pasting condition.” An application to MacDonald and Siegel’s canonical investment problem (1986) shows that the standard investment threshold over-estimates the optimal threshold when the lower barrier is absorbing and under-estimates it when the lower barrier is reflecting.investment; uncertainty; irreversibility; barriers; real options

Simulation-Based Exact Tests for Jump-Diffusions with Unidentified Nuisance Parameters. An Application to Commodities Spot Prices

In this paper, we propose to use the Monte-Carlo (MC) test technique to obtain valid p-values when testing for the presence of discontinuities in jump-diffusion models. Indeed, the LR statistic used to test for discontinuities has typically a complex non-standard distribution, for at least two reasons: the jump frequency parameter lies on the boundary of its domain, and unidentified nuisance parameters intervene under the null hypothesis. We show that, if no other (identified) nuisance parameters are present (e.g. the geometric Brownian motion case), the proposed p-value is finite sample exact. Otherwise, we derive nuisance-parameter free bounds on the null distribution of the LR and obtain exact bounds p-values. We illustrate our approach with four classes of jump diffusion models (geometric Brownian motion and logarithmic Ornstein-Uhlenbeck, with and without a GARCH(1,1) error structure), which we apply to weekly and monthly spot prices of non-precious metals, gold, and crude oil. We find significant jumps in all weekly time series, but only in a few monthly time series.

Multi-Sample Thermobalance for Rapid Cyclic Oxidation Under Controlled Atmosphere

When testing the resistance to oxidation of high temperature materials, the cyclic oxidation test is used as a reference because it integrates isothermal oxidation kinetics, oxide scale adherence, mechanical stresses, metallic alloy and oxide mechanical behavior and their evolution with time, in conditions close to the actual conditions of use. To fill the gap between the measurements of physical data (oxidation kinetics, interfacial energy, oxide toughness, growth stresses, coefficients of thermal expansion, mechanical properties of the alloy under the oxide scale,...) and the cyclic oxidation test, comprehensive scientific work is necessary, but also technological development and understanding of the practice of the cyclic oxidation test. This paper presents a new experimental tool, which allows the simultaneous measurement of the mass of several samples placed in the same controlled atmosphere during fast thermal cycles. This multi-sample thermobalance is described, in association with the description of the measurement methodology (i.e. “cyclic thermogravimetry”). First tests of performance of the apparatus are given, including heating and cooling rates and continuous Samass measurements for a P91 alloy

Meromorphy and topology of localized solutions in the Thomas–MHD model

The one-dimensional MHD system first introduced by J.H. Thomas [Phys. Fluids 11, 1245 (1968)] as a model of the dynamo effect is thoroughly studied in the limit of large magnetic Prandtl number. The focus is on two types of localized solutions involving shocks (antishocks) and hollow (bump) waves. Numerical simulations suggest phenomenological rules concerning their generation, stability and basin of attraction. Their topology, amplitude and thickness are compared favourably with those of the meromorphic travelling waves, which are obtained exactly, and respectively those of asymptotic descriptions involving rational or degenerate elliptic functions. The meromorphy bars the existence of certain configurations, while others are explained by assuming imaginary residues. These explanations are tested using the numerical amplitude and phase of the Fourier transforms as probes of the analyticity properties. Theoretically, the proof of the partial integrability backs up the role ascribed to meromorphy. Practically, predictions are derived for MHD plasmas