Valuation of Financial Derivatives Subject to Liquidity Risk

Valuation of financial derivatives subject to liquidity risk remains an open problem in finance. This dissertation focuses on the valuation of European-style call option under limited market liquidity through the dynamic management of a portfolio of assets. We investigate liquidity from three perspectives: market breadth, depth, and immediacy. We present a general framework of valuation based on the optimal realization of a performance index relative to the set of all feasible portfolio trajectories. Numerical examples are then presented and analyzed that show option price increases as the market transitions from liquid to less liquid state. Furthermore, buying and selling activities, based on our optimal trading strategy, decrease as the market becomes less liquid because the gain from more frequent rebalancing of the portfolio is not able to offset the liquidity risk

Generalizing Ruth-Aaron Numbers

A Ruth-Aaron number is such that the sum of its prime divisors, counted with multiplicity, equals the sum of the prime divisors of its successor. They have been an interest of many number theorists since the famous 1974 baseball game gave them the elegant name after two baseball stars. Many of their properties were first discussed by Erdős and Pomerance in 1978. We generalize their results in two directions: by raising prime factors to a power and allowing a small difference between the two sums. We prove the density of power Ruth-Aaron numbers is zero (we provide a precise bound in terms of iterations and powers of logarithms), and prove similar results for almost Ruth-Aaron numbers (these are pairs of integers such that the sum of their prime powers differ by a fixed, slowly growing function). Moreover, we further the discussion of the infinitude of Ruth-Aaron numbers and provide a few possible directions for future study

Pertussis Toxin-sensitive Activation of Phospholipase C by the C5a and fMet-Leu-Phe Receptors

Signal transduction pathways that mediate C5a and fMet-Leu-Phe (fMLP)-induced pertussis toxin (PTx)-sensitive activation of phospholipase C (PLC) have been investigated using a cotransfection assay system in COS-7 cells. The abilities of the receptors for C5a and fMLP to activate PLC beta 2 and PLC beta 3 through the Gbeta gamma subunits of endogenous Gi proteins in COS-7 cells were tested because both PLC beta 2 and PLC beta 3 were shown to be activated by the beta gamma subunits of G proteins in in vitro reconstitution assays. Neither of the receptors can activate endogenous PLC beta 3 or recombinant PLC beta 3 in transfected COS-7 cells. However, both receptors can clearly activate PLC beta 2 in a PTx-sensitive manner, suggesting that the receptors may interact with endogenous PTx-sensitive G proteins and activate PLC beta 2 probably through the Gbeta gamma subunits. These findings were further corroborated by the results that PLC beta 3 could only be slightly activated by Gbeta 1gamma 1 or Gbeta 1gamma 5 in the cotransfection assay, whereas the Gbeta gamma subunits strongly activated PLC beta 2 under the same conditions. PLC beta 3 can be activated by Galpha q, Galpha 11, and Galpha 16 in the cotransfection assay. In addition, the Ggamma 2 and Ggamma 3 mutants with substitution of the C-terminal Cys residue by a Ser residue, which can inhibit wild type Gbeta gamma -mediated activation of PLC beta 2, were able to inhibit C5a or fMLP-mediated activation of PLC beta 2. These Ggamma mutants, however, showed little effect on m1-muscarinic receptor-mediated PLC activation, which is mediated by the Gq class of G proteins. These results all confirm that the Gbeta gamma subunits are involved in PLC beta 2 activation by the two chemoattractant receptors and suggest that in COS-7 cells activation of PLC beta 3 by Gbeta gamma may not be the primary pathway for the receptors

The Restrictive Factors and Practical Path of Sports-Medical Integration Under the Background of COVID-19 Pandemic

This paper explored the restrictive factors of realizing the integration of sports and medicine in China under the background of “COVID-19 pandemic” and analyzed the path of realizing the integration of sports and medicine by combining it with “Healthy China” strategy and “National Fitness Program”. We used document and expert interview method. In the new era, people’s desire for a better life has become the most extensive demand, and the sudden outbreak of epidemic makes people’s demand for health become the first demand. The importance of people’s health raises “Healthy China” as the national development strategy, which has become the opportunities to realize the “integration of sports and medicine”. At present, China has formed three “sports-medical integration” models: the combination of the government and the market, the fitness guidance center of the hospital and the physique monitoring center of the community. Among them, the model of community physique monitoring center is in line with China\u27s national conditions, but the development of this model still needs policy and financial support. At present, China’s “integration of sports and medicine” is still facing a few challenges: a) The conceptual understanding remains weak while the belief to medical treatment and negligence of sports is strong; b) There is lack of standards of sports knowledge and skills, so it is difficult to reach a consensus; c) The sports and medicine industry has a low level of integration and lacks an integrated environment. The impact of the COVID-19 pandemic is not only a challenge but also an opportunity to realize the integration of sports and medicine. At present, with the support of national strategy, “integration of sports and medicine” is in the best historical development opportunity. At the same time, however, it also faces a series of contradictions. In this regard, it is necessary to deepen the essence of the two to carry out conceptual innovation and enhance the national recognition of the functional value of “sports-medicine integration”. Strategies include cooperating with sports medicine institutions to build a service platform, strengthening the integration of sports and medicine disciplines while building a qualification certification system and cultivating comprehensive talents, and improving the environment of “integration of sports and medicine” with building the foundation of harmonious symbiosis

Stationary distribution of stochastic SIRS epidemic model with standard incidence

We study stochastic versions of a deterministic SIRS (Susceptible, Infective, Recovered, Susceptible) epidemic model with standard incidence. We study the existence of a stationary distribution of stochastic system by the theory of integral Markov semigroup. We prove the distribution densities of the solutions can converge to an invariant density in L1. This shows the system is ergodic. The presented results are demonstrated by numerical simulations

Prognostic value of osteopontin splice variant-c expression in breast cancers: a meta-analysis

Objectives. Osteopontin (OPN) is overexpressed in breast cancers, while its clinical and prognostic significance remained unclear. This study aimed to assess the prognostic value of OPN, especially its splice variants, in breast cancers. Methods. Data were extracted from eligible studies concerning the OPN and OPN-c expression in breast cancer patients and were used to calculate the association between OPN/OPN-c and survival. Two reviewer teams independently screened the literatures according to the inclusion and exclusion criteria based on quality evaluation. Following the processes of data extraction, assessment, and transformation, meta-analysis was carried out via RevMan 5.3 software. Results. A total of ten studies involving 1,567 patients were included. The results demonstrated that high level OPN indicated a poor outcome in the OS (HR = 2.22, 95% CI: 1.23–4.00, and ; random-effects model) with heterogeneity (%) of breast cancer patients. High level OPN-c appeared to be more significantly associated with poor survival (HR = 2.14, 95% CI: 1.51–3.04, and ; fixed-effects model) with undetected heterogeneity (%). Conclusions. Our analyses indicated that both OPN and OPN-c could be considered as prognostic markers for breast cancers. The high level of OPN-c was suggested to be more reliably associated with poor survival in breast cancer patients