Stochastic Analysis For Problems In Mathematical Finance and Economics

This thesis is the study of two different problems in mathematical finance. In the first chapter, we investigate optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A non-standard stochastic differential equation, with neither Lipschitz continuity nor linear growth, specifies the dynamics of the controlled state process. A mixture of probabilistic arguments are used to construct the state process, and establish its non-explosiveness and strict positivity. This leads to the optimality of a feedback consumption process, defined in terms of the value function and the state process. Based on additional viscosity solutions techniques, we characterize the value function as the unique classical solution to a nonlinear elliptic equation, among an appropriate class of functions. This characterization involves a condition on the limiting behavior of the value function at the origin, which is the key to dealing with unbounded consumptions. Finally, relaxing the boundedness constraint is shown to increase, strictly, the expected utility at all wealth levels. In the second chapter, in a discrete-time financial market, a generalized duality is established for model-free superhedging, given marginal distributions of the underlying asset. Contrary to prior studies, we do not require contingent claims to be upper semicontinuous, allowing for upper semi-analytic ones. The generalized duality stipulates an extended version of risk-neutral pricing. To compute the model-free superhedging price, one needs to find the supremum of expected values of a contingent claim, evaluated it not directly under martingale (risk-neutral) measures, but along sequences of measures that converge, in an appropriate sense, to martingale ones. To derive the main result, we first establish a portfolio-constrained duality for upper semi-analytic contingent claims, relying on Choquet's capacitability theorem. As we gradually fade out the portfolio constraint, the generalized duality emerges through delicate probabilistic estimations.</p

Evaluation of parenteral nutritional support in the surgical and medical wards of a referral teaching hospital

BACKGROUND AND PURPOSE: Malnutrition is a common problem in patients who are hospitalized in surgical and medical wards. Surgical patients, geriatric populations and individuals with severe illness are more vulnerable to malnutrition during their hospitalization course. The purpose of this study was evaluation of parenteral nutrition services in a referral teaching hospital, Tehran, Iran. METHOD: Medical records of 72 patients who received parenteral nutrition during one year period in different surgical and medical wards of Imam Khomeini hospital were reviewed retrospectively by clinical pharmacists. Criteria for initiation of parenteral nutrition, selection of appropriate formulation and monitoring parameters were assessed based on the American Society of Parenteral and Enteral Nutrition recommendations. RESULTS: Based on the patients' anthropometric parameters and serum albumin levels, 4.2%, 75% and 20.8% of the patients were well-nourished, moderately malnourished and severely malnourished respectively at the hospital admission and before nutritional support. Adequate calorie, protein, carbohydrate and lipid supports were achieved in 21.1%, 32.4%, 23.7% and 10.5% of the patients respectively. About 91% of the patients experienced at least one complication of the nutritional support. CONCLUSION: In this evaluation, several errors in assessment, establishing goals, and monitoring of parenteral nutrition regimens have been detected. Approximately all of the patients did not receive to the trace elements supports goals

Investigando o efeito do alinhamento entre o gerenciamento de portfólios e a estratégia da organização no sucesso de portfólios em uma empresa de petróleo e gás

The aim of this study was the effect of alignment between portfolios management and strategy of the organization on portfolios success in Iranian Oil &amp; Gas Company. This study was applied and correlational. In the first phase, using previous literature and interviewing the elites, the indicators were identified then proposed a questionnaire, the validity of which was confirmed using experts’ ideas as well as convergent validity and the reliability of questionnaires was obtained as 0.81 using Cronbach’s alpha. In the next phase, to test model and investigate the alignment status of research statistical population that is the company, 99 managers and employees were selected as sample. To analyze data, structural equation test through PLS software was used. The results showed that:1-Strategic alignment of portfolios and the strategy of organization affects the portfolio’s success positively and has a significant relationship with it.2-Strategic alignment of portfolios and the strategy of organization affects the realization of organization benefits positively and has a significant relationship with it. 3-The portfolios success aff ects the realization of organization benefits positively and has a significant relationship with it.El objetivo de este estudio fue el efecto de la alineación entre la gestión de carteras y la estrategia de la organización sobre el éxito de las carteras en Iranian Oil &amp; Gas Company. Este estudio fue aplicado y correlacional. En la primera fase, utilizando literatura previa y entrevistando a las élites, se identificaron los indicadores y luego se propuso un cuestionario, cuya validez se confirmó con ideas de expertos y validez convergente, y la confiabilidad de los cuestionarios se obtuvo como 0,81 usando alfa de Cronbach. En la siguiente fase, para probar el modelo e investigar el estado de alineación de la población estadística de investigación que es la empresa, se seleccionaron 99 gerentes y empleados como muestra. Para analizar los datos, se utilizó la prueba de ecuación estructural a través del software PLS. Los resultados mostraron que:1-La alineación estratégica de las carteras y la estrategia de organización afecta positivamente el éxito de la cartera y tiene una relación significativa con ella.2-La alineación estratégica de las carteras y la estrategia de organización afecta positivamente&nbsp;la realización de los beneficios de la organización y tiene una relación significativa con ella.3-El éxito de las carteras afecta positivamente la realización de los beneficios de la organización y tiene una relación significativa con ella.O objetivo deste estudo foi o efeito do alinhamento entre o gerenciamento de portfólios e a estratégia da organização sobre o sucesso dos portfólios na Iranian Oil &amp; Gas Company. Este estudo foi aplicado e correlacional. Na primeira fase, utilizando a literatura prévia e entrevistando as elites, os indicadores foram identificados e, em seguida, proposto um questionário, cuja validade foi confirmada por meio de idéias de especialistas e validade convergente e a confiabilidade dos questionários foi obtida em 0,81 usando o alfa de Cronbach. Na fase seguinte, para testar o modelo e investigar o status de alinhamento da população estatística da pesquisa que é a empresa, 99 gestores e funcionários foram selecionados como amostra. Para análise dos dados, foi utilizado o teste de equações estruturais por meio do software PLS. Os resultados mostraram que:1-Alinhamento estratégico de portfólios e a estratégia de organização afeta positivamente o sucesso do portfólio e tem uma relação significativa com ele.2-O alinhamento estratégico de portfólios e a estratégia de organização afetam positivamente a realização dos benefícios da organização e possuem uma relação significativa com ela.3 - O sucesso das carteiras afeta positivamente a realização dos benefícios da organização e tem relação significativa com ela

The Assessment of Health-Promoting Lifestyle Status and Its Determinants among Students of Iran University of Medical Sciences

Careful assessment of lifestyle status among students is a necessity for identifying lifestyle problems and, it is an essential prerequisite for more efficient planning and implementing health promotion interventions among them. This study performed to estimate the current status of a health-promoting lifestyle among students of Iran University of Medical Sciences. This cross-sectional study was performed on 250 students of Iran University of Medical Sciences. By performing a proportional stratified random sampling method according to the number of students in each academic discipline, samples were chosen. The data gathering tool was a two-part questionnaire. The first part was related to demographic and socioeconomic information. The second part consisted of the Health-Promoting Lifestyle Profile (HPLP-II) questionnaire. The data were analyzed using SPSS version 23 through descriptive and inferential statistics. The results were statistically observed as significant at p < 0.05. The mean score of health-promoting lifestyle was 124.36 ± 18.41. The highest mean score was for the nutrition dimension (23.67±4.91) and the lowest was for the physical activity dimension (15.08±5.16). This research showed that a statistical proper correlation was found between marital status and spiritual growth. Also, there was a relationship between academic discipline and health responsibility. Additionally, another statistical significant relationship between financial status and health-promoting lifestyle, health responsibility, spiritual growth, and stress management was observed. Since the status of a health-promoting lifestyle is not satisfactory, a wide range of planning and implementing health interventions are needed to improve the health-promoting lifestyle among the students

The Optimal Number of Hospital Beds Under Uncertainty: A Costs Management Approach

Equipping hospital beds uses a great deal of a hospital''''s resources. Therefore, it is essential to consider the hospital beds'''' efficiency. To increase its efficiency, a fuzzy unrestricted model for managing hospital expenses is presented in this paper. The lack of beds in hospitals leads to patients’ admission loss and consecutively profit loss. On the other hand, increasing the bed count leads to an increase in equipment expenses. Therefore, in order to determine optimal bed capacity, it is of utmost importance to consider these two costs simultaneously. In our paper, hospital admission system is modeled with a multi-server queuing system (M/M/K). Therefore, to calculate the total cost function, limiting probabilities of multi-server queueing model is used. Furthermore, due to uncertain nature of parameters, such as interest rate and hospitalization profit in various future time periods, these uncertainties are covered by fuzzy logic. Finally, to determine the optimal bed count, Lee and Li''''s fuzzy ranking method is used. This model is implemented ona case study. Its goal is to determine the optimal bed count for emergency unit of Razi hospital in Torbat Heydarieh. Considering the high capability of Markovian chains in modeling different circumstances and the various queueing models, the proposed model can be extended for various hospital units

Distribution of Bupivacaine in Epidural Space

Background: There is no consensus regarding the spread of local anesthesia in thoracic epidural space to obtain regional analgesia or anesthesia. We aimed to determine the distribution of Bupivacaine injected into the thoracic epidural space to evaluate its cranial or caudal spread in patients undergoing epidural anesthesia.Materials and Methods: In a prospective clinical trial, thirty adults patients (12 males and 18 females) with ASA class I and II, scheduled for elective cholecystectomy under thoracic epidural anesthesia with 0.5% Isobaric Bupivacaine were studied. Clinical and radiological outcomes were evaluated to assess the correlation between the volume of the local anesthetic injected to the thoracic epidural space and the extension of its spread within the epidural space. Immediately after insertion and fixation of epidural catheter, patients were transferred to MRI unit to receive 8 mL of 5% Bupivacaine plus 1 mL Magnevist through the epidural catheter. Then, the patterns of spread were evaluated. Data were obtained prospectively during the procedure.Results: Mean distribution of bupivacaine in thoracic epidural space was 0.64 level/ml of local anesthetics and the average of spread was 5.21 levels. The mean spread of bupivacaine was more in females (5.5 ± 1.1) than males (4.8 ± 1.1); but the difference was not significant. Unlike Patients’ age and weight, the height and body mass index had a significant negative correlation with the distribution of Bupivacaine.Conclusion: Distribution of Bupivacaine in epidural space in female patients is more than male ones and the tendency of spread is more toward the cephalad direction than caudal.Keywords: Bupivacaine distribution, Epidural anesthesia, Local Anesthesia, Bupivacaine, Magnevis

Optimal Consumption in the Stochastic Ramsey Problem without Boundedness Constraints

This paper investigates optimal consumption in the stochastic Ramsey problem with the Cobb-Douglas production function. Contrary to prior studies, we allow for general consumption processes, without any a priori boundedness constraint. A non-standard stochastic differential equation, with neither Lipschitz continuity nor linear growth, specifies the dynamics of the controlled state process. A mixture of probabilistic arguments are used to construct the state process, and establish its non-explosiveness and strict positivity. This leads to the optimality of a feedback consumption process, defined in terms of the value function and the state process. Based on additional viscosity solutions techniques, we characterize the value function as the unique classical solution to a nonlinear elliptic equation, among an appropriate class of functions. This characterization involves a condition on the limiting behavior of the value function at the origin, which is the key to dealing with unbounded consumptions. Finally, relaxing the boundedness constraint is shown to increase, strictly, the expected utility at all wealth levels.</p