scholarly journals The longest path in the Price model

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Tim S. Evans ◽  
Lucille Calmon ◽  
Vaiva Vasiliauskaite
Keyword(s):  
2021 ◽  
Vol 53 (2) ◽  
pp. 335-369
Author(s):  
Christian Meier ◽  
Lingfei Li ◽  
Gongqiu Zhang

AbstractWe develop a continuous-time Markov chain (CTMC) approximation of one-dimensional diffusions with sticky boundary or interior points. Approximate solutions to the action of the Feynman–Kac operator associated with a sticky diffusion and first passage probabilities are obtained using matrix exponentials. We show how to compute matrix exponentials efficiently and prove that a carefully designed scheme achieves second-order convergence. We also propose a scheme based on CTMC approximation for the simulation of sticky diffusions, for which the Euler scheme may completely fail. The efficiency of our method and its advantages over alternative approaches are illustrated in the context of bond pricing in a sticky short-rate model for a low-interest environment and option pricing under a geometric Brownian motion price model with a sticky interior point.


Author(s):  
Yonglin Zhang ◽  
Xiao Fu ◽  
Chencan Lv ◽  
Shanlin Li

Population agglomeration and real estate development encroach on public green spaces, threatening human settlement equity and perceptual experience. Perceived greenery is a vital interface for residents to interact with the urban eco-environment. Nevertheless, the economic premiums and spatial scale of such greenery have not been fully studied because a comprehensive quantitative framework is difficult to obtain. Here, taking advantage of big geodata and deep learning to quantify public perceived greenery, we integrate a multiscale GWR (MGWR) and a hedonic price model (HPM) and propose an analytic framework to explore the premium of perceived greenery and its spatial pattern at the neighborhood scale. Our empirical study in Beijing demonstrated that (1) MGWR-based HPM can lead to good performance and increase understanding of the spatial premium effect of perceived greenery; (2) for every 1% increase in neighborhood-level perceived greenery, economic premiums increase by 4.1% (115,862 RMB) on average; and (3) the premium of perceived greenery is spatially imbalanced and linearly decreases with location, which is caused by Beijing’s monocentric development pattern. Our framework provides analytical tools for measuring and mapping the capitalization of perceived greenery. Furthermore, the empirical results can provide positive implications for establishing equitable housing policies and livable neighborhoods.


Author(s):  
Jinghai Shao ◽  
Sovan Mitra ◽  
Andreas Karathanasopoulos

AbstractIn this paper we provide a stock price model that explicitly incorporates credit risk, under a stochastic optimal control system. The stock price model also incorporates the managerial control of credit risk through a control policy in the stochastic system. We provide explicit conditions on the existence of optimal feedback controls for the stock price model with credit risk. We prove the continuity of the value function, and then prove the dynamic programming principle for our system. Finally, we prove the Viscosity Solution of the Hamilton–Jacobi–Bellman equation. This paper is particularly relevant to industry, as the impact of credit risk upon stock prices has been prominent since the commencement of the Global Financial Crisis.


Author(s):  
José-María Montero ◽  
Gema Fernández-Avilés

2000 ◽  
Vol 21 (15) ◽  
pp. 2943-2949 ◽  
Author(s):  
A. Rastogi ◽  
N. Kalra ◽  
P. K. Agarwal ◽  
S. K. Sharma ◽  
R. C. Harit ◽  
...  

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