Optimal dividend and capital injection under spectrally positive Markov additive models

This paper studies De Finetti's optimal dividend problem with capital injection under spectrally positive Markov additive models. Based on dynamic programming principle, we first study an auxiliary singular control problem with a final payoff at an exponential random time. The double barrier strategy is shown to be optimal and the optimal barriers are characterized in analytical form using fluctuation identities of spectrally positive Levy processes. We then transform the original problem under spectrally positive Markov additive models into an equivalent series of local optimization problems with the final payoff at the regime-switching time. The optimality of the regime-modulated double barrier strategy can be confirmed for the original problem using results from the auxiliary problem and the fixed point argument for recursive iterations.Comment: Keywords: Spectrally positive Levy process, regime switching, De Finetti's optimal dividend, capital injection, double barrier strategy, singular contro

On De Finetti's control under Poisson observations: optimality of a double barrier strategy in a Markov additive model

In this paper we consider the De Finetti's optimal dividend and capital injection problem under a Markov additive model. We assume that the surplus process before dividends and capital injections follows a spectrally positive Markov additive process. Dividend payments are made only at the jump times of an independent Poisson process. Capitals are required to be injected whenever needed to ensure a non-negative surplus process to avoid bankruptcy. Our purpose is to characterize the optimal periodic dividend and capital injection strategy that maximizes the expected total discounted dividends subtracted by the total discounted costs of capital injection. To this end, we first consider an auxiliary optimal periodic dividend and capital injection problem with final payoff under a single spectrally positive L\'evy process and conjecture that the optimal strategy is a double barrier strategy. Using the fluctuation theory and excursion-theoretical approach of the spectrally positive L\'evy process and the Hamilton-Jacobi-Bellman inequality approach of the control theory, we are able to verify the conjecture that some double barrier periodic dividend and capital injection strategy solves the auxiliary problem. With the results for the auxiliary control problem and a fixed point argument for recursive iterations induced by the dynamic programming principle, the optimality of a regime-modulated double barrier periodic dividend and capital injection strategy is proved for our target control problem.Comment: arXiv admin note: text overlap with arXiv:2207.0266

Optimal portfolio under ratio-type periodic evaluation in incomplete markets with stochastic factors

This paper studies a type of periodic utility maximization for portfolio management in an incomplete market model, where the underlying price diffusion process depends on some external stochastic factors. The portfolio performance is periodically evaluated on the relative ratio of two adjacent wealth levels over an infinite horizon. For both power and logarithmic utilities, we formulate the auxiliary one-period optimization problems with modified utility functions, for which we develop the martingale duality approach to establish the existence of the optimal portfolio processes and the dual minimizers can be identified as the "least favorable" completion of the market. With the help of the duality results in the auxiliary problems and some fixed point arguments, we further derive and verify the optimal portfolio processes in a periodic manner for the original periodic evaluation problems over an infinite horizon.Comment: 28 pages, 33 conferenc

htSNPer1.0: software for haplotype block partition and htSNPs selection

BACKGROUND: There is recently great interest in haplotype block structure and haplotype tagging SNPs (htSNPs) in the human genome for its implication on htSNPs-based association mapping strategy for complex disease. Different definitions have been used to characterize the haplotype block structure in the human genome, and several different performance criteria and algorithms have been suggested on htSNPs selection. RESULTS: A heuristic algorithm, generalized branch-and-bound algorithm, is applied to the searching of minimal set of haplotype tagging SNPs (htSNPs) according to different htSNPs performance criteria. We develop a software htSNPer1.0 to implement the algorithm, and integrate three htSNPs performance criteria and four haplotype block definitions for haplotype block partitioning. It is a software with powerful Graphical User Interface (GUI), which can be used to characterize the haplotype block structure and select htSNPs in the candidate gene or interested genomic regions. It can find the global optimization with only a fraction of the computing time consumed by exhaustive searching algorithm. CONCLUSION: htSNPer1.0 allows molecular geneticists to perform haplotype block analysis and htSNPs selection using different definitions and performance criteria. The software is a powerful tool for those focusing on association mapping based on strategy of haplotype block and htSNPs

Duet: efficient and scalable hybriD neUral rElation undersTanding

Learned cardinality estimation methods have achieved high precision compared to traditional methods. Among learned methods, query-driven approaches face the data and workload drift problem for a long time. Although both query-driven and hybrid methods are proposed to avoid this problem, even the state-of-the-art of them suffer from high training and estimation costs, limited scalability, instability, and long-tailed distribution problem on high cardinality and high-dimensional tables, which seriously affects the practical application of learned cardinality estimators. In this paper, we prove that most of these problems are directly caused by the widely used progressive sampling. We solve this problem by introducing predicates information into the autoregressive model and propose Duet, a stable, efficient, and scalable hybrid method to estimate cardinality directly without sampling or any non-differentiable process, which can not only reduces the inference complexity from O(n) to O(1) compared to Naru and UAE but also achieve higher accuracy on high cardinality and high-dimensional tables. Experimental results show that Duet can achieve all the design goals above and be much more practical and even has a lower inference cost on CPU than that of most learned methods on GPU

Q-Instruct: Improving Low-level Visual Abilities for Multi-modality Foundation Models

Multi-modality foundation models, as represented by GPT-4V, have brought a new paradigm for low-level visual perception and understanding tasks, that can respond to a broad range of natural human instructions in a model. While existing foundation models have shown exciting potentials on low-level visual tasks, their related abilities are still preliminary and need to be improved. In order to enhance these models, we conduct a large-scale subjective experiment collecting a vast number of real human feedbacks on low-level vision. Each feedback follows a pathway that starts with a detailed description on the low-level visual appearance (*e.g. clarity, color, brightness* of an image, and ends with an overall conclusion, with an average length of 45 words. The constructed **Q-Pathway** dataset includes 58K detailed human feedbacks on 18,973 images with diverse low-level appearance. Moreover, to enable foundation models to robustly respond to diverse types of questions, we design a GPT-participated conversion to process these feedbacks into diverse-format 200K instruction-response pairs. Experimental results indicate that the **Q-Instruct** consistently elevates low-level perception and understanding abilities across several foundational models. We anticipate that our datasets can pave the way for a future that general intelligence can perceive, understand low-level visual appearance and evaluate visual quality like a human. Our dataset, model zoo, and demo is published at: https://q-future.github.io/Q-Instruct.Comment: 16 pages, 11 figures, page 12-16 as appendi

A Prospective Randomized Study of the Radiotherapy Volume for Limited-stage Small Cell Lung Cancer: A Preliminary Report

Background and objective Controversies exists with regard to target volumes as far as thoracic radiotherapy (TRT) is concerned in the multimodality treatment for limited-stage small cell lung cancer (LSCLC). The aim of this study is to prospectively compare the local control rate, toxicity profiles, and overall survival (OS) between patients received different target volumes irradiation after induction chemotherapy. Methods LSCLC patients received 2 cycles of etoposide and cisplatin (EP) induction chemotherapy and were randomly assigned to receive TRT to either the post- or pre-chemotherapy tumor extent (GTV-T) as study arm and control arm, CTV-N included the positive nodal drainage area for both arms. One to 2 weeks after induction chemotherapy, 45 Gy/30 Fx/19 d TRT was administered concurrently with the third cycle of EP regimen. After that, additional 3 cycles of EP consolidation were administered. Prophylactic cranial irradiation (PCI) was administered to patients with a complete response. Results Thirty-seven and 40 patients were randomly assigned to study arm and control arm. The local recurrence rates were 32.4% and 28.2% respectively (P=0.80); the isolated nodal failure (INF) rate were 3.0% and 2.6% respectively (P=0.91); all INF sites were in the ipsilateral supraclavicular fossa. Medastinal N3 disease was the risk factor for INF (P=0.02, OR=14.13, 95%CI: 1.47-136.13). During radiotherapy, grade I, II weight loss was observed in 29.4%, 5.9% and 56.4%, 7.7% patients respectively (P=0.04). Grade 0-I and II-III late pulmonary injury was developed in 97.1%, 2.9% and 86.4%, 15.4% patients respectively (P=0.07). Median survival time was 22.1 months and 26.9 months respectively. The 1 to 3-year OS were 77.9%, 44.4%, 37.3% and 75.8%, 56.3%, 41.7% respectively (P=0.79). Conclusion The preliminary results of this study indicate that irradiant the post-chemotherapy tumor extent (GTV-T) and positive nodal drainage area did not decrease local control and overall survival while radiation toxicity was reduced. But the current sample size has not met designed requirements, and further investigation is warranted before final conclusions could be drawn

Information propagation in a non-local model with emergent locality

In this paper, we revisit a "relatively local" model proposed in arXiv:1811.07241, where locality and dimensionality of space only emerges from the entanglement structure of the state the system is in. Various quantities such as butterfly velocity/ entanglement speed can be defined similarly, at least in the regime where locality is well defined and a light cone structure emerges in the correlation between sites. We find that the relations observed between them in local models arXiv:1908.06993 are not respected. In particular, we conjecture that the hierarchy of the interaction over different distances provides different "layers" of light-cones. When long range interactions are sufficiently suppressed, the effective light cones are dominated by linear behaviors with little remnant of non-locality. This could potentially be used as a physical smoking gun for emergent locality in non-local models.Comment: Slightly revised abstract, section 2, section 4.2 and discussio

Lending Motivation Meets Home and Cultural Bias: A Study on Kiva

Online pro-social crowd funding platforms facilitate borrowers from economically weaker locations to access financial supports from lenders globally. However, geographical and cultural distances are still prevailing on these platforms. Loan transactions are more likely to occur between lenders and borrowers in the same country and lenders prefer to fund culturally similar and geographically proximate borrowers. Since, it prevents the borrowers from underrepresented populations to access sufficient loan funding, how to overcome this bias needs to be examined. This study aims to investigate how lenders’ lending motivations affect their lending decisions on the loan requests regarding the regional and cultural differences between lenders and borrowers. We contextualize our study at Kiva.org and lending transactions are retrieved via its API. Lenders’ motivations are mined and categorized based on lenders’ self-stated descriptions. This study potentially contributes to enrich the literature of cross-cultural studies in social lending by studying the effects of lending motivation

Investigations on asymmetric transmittivity of optical devices and different diode-like behaviors

Summary: This study theoretically proved that although reciprocal optical devices can show asymmetric transmittivity (AT) under controlled incident modes (i.e., conditional AT), they cannot guarantee AT with arbitrary incident light modes, whereas only nonreciprocal optical devices can possibly guarantee AT. Besides, the thermodynamics of both reciprocal and nonreciprocal optical devices were discussed to show that the second law of thermodynamics is valid anyway. Furthermore, the diode-like behaviors of optical and electronic devices were compared. Electrons are identical to electronic devices, so electronic devices could have asymmetric conductance regardless of electrons. In contrast, electromagnetic waves are different from optical devices as transmittivity of different modes can be different, so reciprocal optical devices showing conditional AT cannot guarantee AT when incident modes are arbitrary. The mathematical proof and characteristic comparisons between electronic and optical diodes, which are firstly presented here, should help clarifying the necessary nonreciprocity required for being optical diodes