| 1. |
- Aly, Sidi Mohamed, et al.
(author)
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Market making and portfolio liquidation under uncertainty
- 2014
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In: International Journal of Theoretical and Applied Finance. - 1793-6322 .- 0219-0249. ; 17:5
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Journal article (peer-reviewed)abstract
- Market making and optimal portfolio liquidation in the context of electronic limit order books are of considerably practical importance for high frequency (HF) market makers as well as more traditional brokerage firms supplying optimal execution services for clients. In general, the two problems are based on probabilistic models defined on certain reference probability spaces. However, due to uncertainty in model parameters or in periods of extreme market turmoil, ambiguity concerning the correct underlying probability measure may appear and an assessment of model risk, as well as the uncertainty on the choice of the model itself, becomes important, as for a market maker or a trader attempting to liquidate large positions, the uncertainty may result in unexpected consequences due to severe mispricing. This paper focuses on the market making and the optimal liquidation problems using limit orders, accounting for model risk or uncertainty. Both are formulated as stochastic optimal control problems, with the controls being the spreads, relative to a reference price, at which orders are placed. The models consider uncertainty in both the drift and volatility of the underlying reference price, for the study of the effect of the uncertainty on the behavior of the market maker, accounting also for inventory restriction, as well as on the optimal liquidation using limit orders.
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| 2. |
- Liu, Shudong, et al.
(author)
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An Efficient Inventory Rationing Strategy for Systems with Two Demand Classes and Backordering
- 2015
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In: International Journal of Production Research. - : Informa UK Limited. - 0020-7543 .- 1366-588X. ; 53:20, s. 6136-6142
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Journal article (peer-reviewed)abstract
- For systems with two customer classes and backordering, the formulae for the optimal dynamic critical levels in the literature are too complex to be extended to large values of critical levels. In this paper, an efficient method is introduced to obtain approximate closed-form expressions for the dynamic critical levels, even for large values. It is further verified by numerical results the accuracy of the approximate expressions, from which important managerial insights can be obtained.
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| 3. |
- Liu, Shudong, et al.
(author)
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Multi-class dynamic inventory rationing with stochastic demands and backordering
- 2015
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In: European Journal of Operational Research. - : Elsevier BV. - 0377-2217 .- 1872-6860. ; 244:1, s. 153-163
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Journal article (peer-reviewed)abstract
- Dynamic inventory rationing is considered for systems with multiple demand classes, stationary stochastic demands, and backordering. In the literature, dynamic programming has been often applied to address this type of problems. However, due to the curse of dimensionality, computation is a critical challenge for dynamic programming. In this paper, an innovative two-step approach is proposed based on an idea similar to the certainty equivalence principle. First the deterministic inventory rationing problem is studied, where the future demands are set to be the expectation of the stochastic demand processes. The important properties obtained from solving the problem with the KKT conditions are then used to develop effective dynamic rationing policies for stochastic demands, which gives closed-form expressions for dynamic rationing thresholds. These expressions are easy to calculate and are applicable to any number of demand classes. Numerical results show that the expressions are close to and provide a lower bound for the optimal dynamic thresholds. They also shed light on important managerial insights, for example, the relation between different parameters and the rationing thresholds.
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| 6. |
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| 7. |
- Mikulevicius, Remigijus, et al.
(author)
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Weak Euler Approximation for Ito Diffusion and Jump Processes
- 2015
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In: Stochastic Analysis and Applications. - : Informa UK Limited. - 0736-2994 .- 1532-9356. ; 33:3, s. 549-571
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Journal article (peer-reviewed)abstract
- This article studies the rate of convergence of the weak Euler approximation for Itô diffusion and jump processes with Hölder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in Hölder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence.
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| 8. |
- Nyström, Kaj, 1969-, et al.
(author)
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Hawkes-Based Models for High Frequency Financial Data
- 2022
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In: Journal of the Operational Research Society. - : Taylor & Francis. - 0160-5682 .- 1476-9360. ; 73:10, s. 2168-2185
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Journal article (peer-reviewed)abstract
- Compared with low frequency data, high frequency data exhibit distinct empirical properties,including, for instance, essentially discontinuous evolution paths, time-varying intensities, and self-exciting features. All these make it more challenging to model appropriately the dynamics associatedwith high frequency data such as order arrival and price formation. To capture more accuratelythe microscopic structures and properties pertaining to the limit order books, this paper focuses onmodeling high frequency data using Hawkes processes. Two models, one with exponential kernels andthe other with power-law kernels, are introduced systematically, algorithmized precisely, and comparedwith each other extensively from various perspectives, including the goodness of fit to the original dataand the computational time in searching for the maximum likelihood estimator, with search algorithmbeing taken into consideration as well. To measure the goodness of fit, a number of quantities areproposed. Studies based on both multiple-trading-day data of one stock and multiple-stock data onone trading day indicate that Hawkes processes with slowly-decaying kernels are able to reproduce theintensity of jumps in the price processes more accurately. The results suggest that Hawkes processeswith power-law kernels and their implied long memory nature of self-excitation phenomena could, onthe level of microstructure, serve as a realistic model for high frequency data.
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| 9. |
- Zhang, Changyong
(author)
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An Origin-Based Model for Unique Shortest Path Routing
- 2016
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In: Journal of the Operational Research Society. - : Springer. - 0160-5682 .- 1476-9360. ; 68
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Journal article (peer-reviewed)abstract
- Link weights are the main parameters of shortest path routing protocols, the most commonly used protocols for IP networks. The problem of optimally setting link weights for unique shortest path routing is addressed. Due to the complexity of the constraints involved, there exist challenges to formulate the problem in such a way based on which a more efficient solution algorithm than the existing ones may be developed. In this paper, an exact formulation is first introduced and then mathematically proved correct. It is further illustrated that the formulation has advantages over a prior one in terms of both constraint structure and model size for a proposed decomposition method to solve the problem.
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