Optimal High Frequency Trading with limit and market orders

We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson process of the tick-time clock. We consider a small agent who continuously submits limit buy/sell orders and submits market orders at discrete dates. The objective of the market maker is to maximize her expected utility from revenue over a short term horizon by a tradeoff between limit and market orders, while controlling her inventory position. This is formulated as a mixed regime switching regular/ impulse control problem that we characterize in terms of quasi-variational system by dynamic programming methods. In the case of a mean-variance criterion with martingale reference price or when the asset price follows a Levy process and with exponential utility criterion, the dynamic programming system can be reduced to a system of simple equations involving only the inventory and spread variables. Calibration procedures are derived for estimating the transition matrix and intensity parameters for the spread and for Cox processes modelling the execution of limit orders. Several computational tests are performed both on simulated and real data, and illustrate the impact and profit when considering execution priority in limit orders and market ordersMarket making; limit order book; inventory risk; point process; stochastic control

On-stack replacement, distilled

On-stack replacement (OSR) is essential technology for adaptive optimization, allowing changes to code actively executing in a managed runtime. The engineering aspects of OSR are well-known among VM architects, with several implementations available to date. However, OSR is yet to be explored as a general means to transfer execution between related program versions, which can pave the road to unprecedented applications that stretch beyond VMs. We aim at filling this gap with a constructive and provably correct OSR framework, allowing a class of general-purpose transformation functions to yield a special-purpose replacement. We describe and evaluate an implementation of our technique in LLVM. As a novel application of OSR, we present a feasibility study on debugging of optimized code, showing how our techniques can be used to fix variables holding incorrect values at breakpoints due to optimizations