Continuous time mean-variance portfolio selection with nonlinear wealth equations and random coefficients

This paper concerns the continuous time mean-variance portfolio selection problem with a special nonlinear wealth equation. This nonlinear wealth equation has nonsmooth random coefficients and the dual method developed in [7] does not work. To apply the completion of squares technique, we introduce two Riccati equations to cope with the positive and negative part of the wealth process separately. We obtain the efficient portfolio strategy and efficient frontier for this problem. Finally, we find the appropriate sub-derivative claimed in [7] using convex duality method.Comment: arXiv admin note: text overlap with arXiv:1606.0548

Structural performance of approach slab and its effect on vehicle induced bridge dynamic response

Differential settlement often occurs between the bridge abutment and the embankment soil. It causes the approach slab to lose its contacts and supports from the soil and the slab will bend in a concave manner. Meanwhile, loads on the slab will also redistribute to the slab ends, which may result in faulting (or bump ) at the slab ends. Once a bump forms, repeating traffic vehicles can deteriorate the expansion joint in turn. In this case, the vehicle receives an initial disturbance before it reaches the bridge. This excitation introduces an extra impact load on the bridge and affects its dynamic responses. The present research targets at the structural performance of the approach slab as well as its effect on the vehicle induced bridge vibration. Firstly, the structural performance of the approach slab is investigated. Based on a parametric study, a correlation among the slab parameters, deflections, internal moments, and the differential settlements has been established. The predicted moments make it much easier to design the approach slab considering different levels of embankment settlements. While flat approach slab may be used for some short span applications, large span length would require a very thick slab. In such case, ribbed approach slabs are proposed, providing advantages over flat slabs. Based on finite element analysis, internal forces and deformations of ribbed slabs have been predicted and their designs are conducted. Secondly, a fully computerized vehicle-bridge coupled model has been developed to analyze the effect of approach slab deformation on bridges’ dynamic response induced by moving vehicles. With this model, the dynamic performance of vehicles and bridges under different road conditions (including approach slab deformation) can be obtained for different numbers and types of vehicles, and different types of bridges. A parametric study reveals that the deformation at the approach span causes significant dynamic responses in short span bridges. AASHTO specifications may underestimate the impact factors for short bridges with uneven joints at the bridge ends. Finally, this study investigated the possibility of using tuned mass damper (TMD) to suppress the vehicle-induced bridge vibration under the condition of uneven bridge expansion joints

Constrained stochastic LQ control with regime switching and application to portfolio selection

This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients, and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and the Markov chain. Using It\^{o}'s lemma for Markov chain, we obtain the optimal state feedback control and optimal cost value explicitly via two new systems of extended stochastic Riccati equations (ESREs). We prove the existence and uniqueness of the two ESREs using tools including multidimensional comparison theorem, truncation function technique, log transformation and the John-Nirenberg inequality. These results are then applied to study mean-variance portfolio selection problems with and without short-selling prohibition with random parameters depending on both the Brownian motion and the Markov chain. Finally, the efficient portfolios and efficient frontiers are presented in closed forms

Comparison theorems for multi-dimensional BSDEs with jumps and applications to constrained stochastic linear-quadratic control

In this paper, we, for the first time, establish two comparison theorems for multi-dimensional backward stochastic differential equations with jumps. Our approach is novel and completely different from the existing results for one-dimensional case. Using these and other delicate tools, we then construct solutions to coupled two-dimensional stochastic Riccati equation with jumps in both standard and singular cases. In the end, these results are applied to solve a cone-constrained stochastic linear-quadratic and a mean-variance portfolio selection problem with jumps. Different from no jump problems, the optimal (relative) state processes may change their signs, which is of course due to the presence of jumps

Constrained monotone mean-variance problem with random coefficients

This paper studies the monotone mean-variance (MMV) problem and the classical mean-variance (MV) problem with convex cone trading constraints in a market with random coefficients. We provide semiclosed optimal strategies and optimal values for both problems via certain backward stochastic differential equations (BSDEs). After noting the links between these BSDEs, we find that the two problems share the same optimal portfolio and optimal value. This generalizes the result of Shen and Zou $[$ SIAM J. Financial Math., 13 (2022), pp. SC99-SC112$]$ from deterministic coefficients to random ones