Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets

The pricing and hedging of financial derivatives have become one of the hot research issues in mathematical finance today. In the case of non-risk neutrality, this article uses the martingale method and probability measurement method to study the pricing method and hedging strategy of financial derivatives. This paper also further studies the hedging strategy of financial derivatives in the incomplete market based on the BSM model and converts the solution of this problem into solving a vector on the Hilbert space to its closure. The problem of space projection is to use projection theory to decompose financial derivatives under a given martingale measure. In the imperfect market, the vertical projection theory is used to obtain the approximate pricing method and hedging strategy of financial derivatives in which the underlying asset follows the martingale process; the projection theory is further expanded, and the pricing problem of financial derivatives under the mixed-asset portfolio is obtained. Approximate pricing of financial derivatives; in the discrete state, the hedging investment strategy of financial derivatives H in the imperfect market is found through the method of variance approximation.

Implicit incentives for fund managers with partial information

We study the optimal asset allocation problem for a fund manager whose compensation depends on the performance of her portfolio with respect to a benchmark. The objective of the manager is to maximise the expected utility of her final wealth. The manager observes the prices but not the values of the market price of risk that drives the expected returns. Estimates of the market price of risk get more precise as more observations are available. We formulate the problem as an optimization under partial information. The particular structure of the incentives makes the objective function not concave. Therefore, we solve the problem by combining the martingale method and a concavification procedure and we obtain the optimal wealth and the investment strategy. A numerical example shows the effect of learning on the optimal strategy.

PORTFOLIO ALLOCATION IN A LEVY-TYPE JUMP-DIFFUSION MODEL WITH NONLIFE INSURANCE RISK

We propose a model that integrates investment, underwriting, and consumption/dividend policy decisions for a nonlife insurer by using a risk control variable related to the wealth-income ratio of the firm. This facilitates the efficient transfer of insurance risk to capital markets since it allows to select simultaneously investments and underwriting volume. The model is particularly valuable for business lines with significant exposure to extreme events and disaster risk, as it accounts for features usually depicted during negative economic shocks and catastrophic events, such as Levy-type jump-diffusion dynamics for the financial log-returns that are in turn correlated with insurance premiums and liabilities, as well as worst-case scenarios in which policyholders in the insurance portfolio report claims with the same severity simultaneously. Using the martingale method, we determine an optimal solvency threshold or wealth-income ratio, and investment strategy that maximizes the expected utility from dividend payouts that follows a (possibly stochastic) consumption clock. We illustrate the main results with numerical examples for log- and power-utility functions, and (bounded variation) tempered stable Levy jumps.

ANALISIS IMBAL HASIL DENGAN AUTOMATIC TRADING DALAM PERSPEKTIF MONEY MANAGEMENT : Studi Eksperimental dengan Expert Advisor pada Pasar Futures

In this study an experimental study was using automatic trading by develop an expert advisors to works with backtesting simulation from January 2010 to December 2019 to research the performance returns of the double moving average cross strategy with 6 pairs from SMA (10.30), SMA (10.50) and SMA (10,100) and EMA (10,30), EMA (10.50), and EMA (10,100). EMA performance (10.30) that given treated 3 types of money management methods, namely fixed lot, fixed % lot, and martingale (1.5x) in the GOLD futures market (XAUUSD) at 1 hour timeframe which will be compared with descriptive analysis. This study shows that the EMA (10.30) without using money management (fixed lot) method shows the most optimal results with a total return 63.5% in the futures market which is higher than the passive strategy. The experimental results show that the fixed % lot method decreases performance with lower returns and increases risk when compared without using money management (fixed lot). While the most optimal money management method is martingale (1.5x) with the achievement of a total return 6,610.56% and a risk adjusted ratio (RAR) at 5.02%. Individually, the method that gives the highest yield is shown by EMA (10.30) on the fixed lot method with a total return of 63.5% and RAR at 2.41%, EMA (10.30) on the fixed sum lot method with a total return of 62.77% and RAR 1.52% and EMA (10.100) with a total return 6.610.56% and RAR 5.02% on the martingale method simulated using expert advisors in the futures market.Keywords: Moving Average, Money Management, Gold, Return, risk adjusted return, Martingale, Fixed Lot, Fixed Ratio, Expert Advisor, Automatic Trading

A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations

Motivated by modelling the data transmission in computer communication networks, we study a Lévy-driven stochastic fluid queueing system where the server may subject to breakdowns and repairs. In addition, the server will leave for a vacation each time when the system is empty. We cast the workload process as a Lévy process modified to have random jumps at two classes of stopping times. By using the properties of Lévy processes and Kella–Whitt martingale method, we derive the limiting distribution of the workload process. Moreover, we investigate the busy period and the correlation structure. Finally, we prove that the stochastic decomposition properties also hold for fluid queues with Lévy input.

Optimal retirement planning under partial information

The present paper analyzes an optimal consumption and investment problem of a retiree with a constant relative risk aversion (CRRA) who faces parameter uncertainty about the financial market. We solve the optimization problem under partial information by making the market observationally complete and consequently applying the martingale method to obtain closed-form solutions to the optimal consumption and investment strategies. Further, we provide some comparative statics and numerical analyses to deeply understand the consumption and investment behavior under partial information. Bearing partial information has little impact on the optimal consumption level, but it makes retirees with an RRA smaller than one invest more riskily, while it makes retirees with an RRA larger than one invest more conservatively.

Gapped PVBS models for all species numbers and dimensions

Product vacua with boundary states (PVBS) are cousins of the Heisenberg XXZ spin model and feature [Formula: see text] particle species on [Formula: see text]. The PVBS models were originally introduced as toy models for the classification of ground state phases. A crucial ingredient for this classification is the existence of a spectral gap above the ground state sector. In this work, we derive a spectral gap for PVBS models at arbitrary species number [Formula: see text] and in arbitrary dimension [Formula: see text] in the perturbative regime of small anisotropy parameters. Instead of using the more common martingale method, the proof verifies a finite-size criterion in the spirit of Knabe.

Size of the Largest Component in a Critical Graph

In this paper, by the branching process and the martingale method, we prove that the size of the largest component in the critical random intersection graph Gn,n5/3,p is asymptotically of order n2/3 and the width of scaling window is n−1/3.