Research articles for the 2019-04-28

A Game Theoretic Setting of Capitation Versus Fee-For-Service Payment Systems
Allison Koenecke

We aim to determine whether a game-theoretic model between an insurer and a healthcare practice yields a predictive equilibrium that incentivizes either player to deviate from a fee-for-service to capitation payment system. Using United States data from various primary care surveys, we find that non-extreme equilibria (i.e., shares of patients, or shares of patient visits, seen under a fee-for-service payment system) can be derived from a Stackelberg game if insurers award a non-linear bonus to practices based on performance. Overall, both insurers and practices can be incentivized to embrace capitation payments somewhat, but potentially at the expense of practice performance.

Dynamic programming for optimal stopping via pseudo-regression
Christian Bayer,Martin Redmann,John Schoenmakers

We introduce new variants of classical regression-based algorithms for optimal stopping problems based on computation of regression coefficients by Monte Carlo approximation of the corresponding $L^2$ inner products instead of the least-squares error functional. Coupled with new proposals for simulation of the underlying samples, we call the approach "pseudo regression". A detailed convergence analysis is provided and it is shown that the approach asymptotically leads to less computational cost for a pre-specified error tolerance, hence to lower complexity. The method is justified by numerical examples.

Multiple Benefits through Smart Home Energy Management Solutions -- A Simulation-Based Case Study of a Single-Family House in Algeria and Germany
Marc Ringel,Roufaida Laidi,Djamel Djenouri

From both global and local perspectives, there are strong reasons to promote energy efficiency. These reasons have prompted leaders in the European Union (EU) and countries of the Middle East and North Africa (MENA) to adopt policies to move their citizenry toward more efficient energy consumption. Energy efficiency policy is typically framed at the national, or transnational level. Policy makers then aim to incentivize microeconomic actors to align their decisions with macroeconomic policy. We suggest another path towards greater energy efficiency: Highlighting individual benefits at microeconomic level. By simulating lighting, heating and cooling operations in a model single-family home equipped with modest automation, we show that individual actors can be led to pursue energy efficiency out of enlightened self-interest. We apply simple-to-use, easily, scalable impact indicators that can be made available to homeowners and serve as intrinsic economic, environmental and social motivators for pursuing energy efficiency. The indicators reveal tangible homeowner benefits realizable under both the market-based pricing structure for energy in Germany and the state-subsidized pricing structure in Algeria. Benefits accrue under both the continental climate regime of Germany and the Mediterranean regime of Algeria, notably in the case that cooling energy needs are considered. Our findings show that smart home technology provides an attractive path for advancing energy efficiency goals. The indicators we assemble can help policy makers both to promote tangible benefits of energy efficiency to individual homeowners, and to identify those investments of public funds that best support individual pursuit of national and transnational energy goals.

No Arbitrage in Continuous Financial Markets
David Criens

We study no arbitrage conditions for financial models in which either the stocks itself or its log returns are continuous Ito processes. More precisely, we derive deterministic conditions for the existence and nonexistence of equivalent (local) martingale measures and strict martingale densities. For models with a random switching mechanism we also study the set of equivalent (local) martingale measures which are structure preserving. In particular, for one dimensional Markov switching models we provide sufficient and necessary conditions for the existence of structure preserving equivalent (local) martingale measures. Mathematically, our proofs are based on local changes of measures and existence and uniqueness conditions.

Optimally stopping at a given distance from the ultimate supremum of a spectrally negative L\'evy process
Mónica B. Carvajal Pinto,Kees van Schaik

We consider the optimal prediction problem of stopping a spectrally negative L\'evy process as close as possible to a given distance $b \geq 0$ from its ultimate supremum, under a squared error penalty function. Under some mild conditions, the solution is fully and explicitly characterised in terms of scale functions. We find that the solution has an interesting non-trivial structure: if $b$ is larger than a certain threshold then it is optimal to stop as soon as the difference between the running supremum and the position of the process exceeds a certain level (less than $b$), while if $b$ is smaller than this threshold then it is optimal to stop immediately (independent of the running supremum and position of the process). We also present some examples.

The Black-Scholes Equation in Presence of Arbitrage
Simone Farinelli,Hideyuki Takada

We apply Geometric Arbitrage Theory to obtain results in Mathematical Finance, which do not need stochastic differential geometry in their formulation. First, for a generic market dynamics given by a multidimensional It\^o's process we specify and prove the equivalence between (NFLVR) and expected utility maximization. As a by-product we provide a geometric characterization of the (NUPBR) condition given by the zero curvature (ZC) condition. Finally, we extend the Black-Scholes PDE to markets allowing arbitrage.