Dealing with the inventory risk: a solution to the market making problem

Market makers continuously set bid and ask quotes for the stocks they have under consideration. Hence they face a complex optimization problem in which their return, based on the bid-ask spread they quote and the frequency at which they indeed provide liquidity, is challenged by the price risk they bear due to their inventory. In this paper, we consider a stochastic control problem similar to the one introduced by Ho and Stoll (J Fin Econ 9(1): 47–73, 1981) and formalized mathematically by Avellaneda and Stoikov (Quant Fin 8(3):217–224, 2008). The market is modeled using a reference price S _t following a Brownian motion with standard deviation σ, arrival rates of buy or sell liquidity-consuming orders depend on the distance to the reference price S _t and a market maker maximizes the expected utility of its P&L over a finite time horizon. We show that the Hamilton–Jacobi–Bellman equations associated to the stochastic optimal control problem can be transformed into a system of linear ordinary differential equations and we solve the market making problem under inventory constraints. We also shed light on the asymptotic behavior of the optimal quotes and propose closed-form approximations based on a spectral characterization of the optimal quotes.     

Measurability of optimal transportation and convergence rate for Landau type interacting particle systems

In this paper, we consider nonlinear diffusion processes driven by space-time white noises, which have an interpretation in terms of partial differential equations. For a specific choice of coefficients, they correspond to the Landau equation arising in kinetic theory. The main goal of the paper is to construct an easily simulable diffusive interacting particle system, converging towards this nonlinear process and to obtain an explicit pathwise rate. This requires to find a significant coupling between finitely many Brownian motions and the infinite dimensional white noise process. The key idea will be to construct the right Brownian motions by pushing forward the white noise processes, through the Brenier map realizing the optimal transport between the law of the nonlinear process, and the empirical measure of independent copies of it. A crucial problem will then be to establish the joint measurability of this optimal transport map, with respect to the space variable and the parameter (time-randomness) that makes the marginals vary. To overcome this point, we shall prove a general measurability result for the mass transportation problem and for the supports of the optimal transfer plans, in the sense of set-valued mappings. This will allow us to construct the coupling and to obtain explicit convergence rates.     

Two-compartment model interacting with proliferating regulatory factor

In this short work, by combining the total cell evolution curve and the two-compartment model, the evolution of one of the subpopulations is simulated while the system interacts with a proliferating regulatory factor.     

Imbedding potentials in tent spaces

We obtain characterizations of positive Borel measures μ on so that the nonisotropic potential space K_α[L^p(dσ)] is imbedded in the tent space T₂^q(dμ), where 1<p,q<+∞. We deduce characterizations for pointwise multipliers of the space H_α^p.     

Miniemulsion copolymerization of vinyl acetate and butyl acrylate. III. Experimental evidence for the role of the cosurfactant

The role of the cosurfactant (hexadecane) in the miniemulsion copolymerization of 50 : 50 molar ratio vinyl acetate–butyl acrylate monomer mixture is analyzed from an experimental point of view. The main factor responsible for the different kinetic behavior between the miniemulsion and conventional emulsion copolymerization processes was found to be the different particle nucleation mechanism operating in each process. Experimental evidence is presented indicating that in the miniemulsion copolymerization particle nucleation takes place in the preformed stable submicron monomer droplets.     

Zr-Porphyrin Metal–Organic Framework as nanoreactor for boosting the formation of hydrogen clathrates

We report the first experimental evidence for rapid formation of hydrogen clathrates under mild pressure and temperature conditions within the cavities of a zirconium-metalloporphyrin framework, specifically PCN-222. PCN-222 has been selected for its 1D mesoporous channels, high water-stability, and proper hydrophilic behavior. Firstly, we optimize a microwave (MW)-assisted method for the synthesis of nanosized PCN-222 particles with precise structure control (exceptional homogeneity in morphology and crystalline phase purity), taking advantage of MW in terms of rapid/homogeneous heating, time and energy savings, as well as potential scalability of the synthetic method. Second, we explore the relevance of the large mesoporous 1D open channels within the PCN-222 to promote the nucleation and growth of confined hydrogen clathrates. Experimental results show that PCN-222 drives the nucleation process at a lower pressure than the bulk system (1.35 kbar vs 2 kbar), with fast kinetics (minutes), using pure water, and with a nearly complete water-to-hydrate conversion. Unfortunately, PCN-222 cannot withstand these high pressures, which lead to a significant alteration of the mesoporous structure while the microporous network remains mainly unchanged.