We revisit the optimal investment and consumption model of Davis and Norman (1990) and Shreve and Soner (1994), following a shadow-price approach similar to that of Kallsen and Muhle-Karbe (2010). Making use of the completeness of the model without transaction costs, we reformulate and reduce the Hamilton-Jacobi-Bellman equation for this singular stochastic control problem to a non-standard free-boundary problem for a first-order ODE with an integral constraint. Having shown that the free boundary problem has a smooth solution, we use it to construct the solution of the original optimal investment/consumption problem in a self-contained manner and without any recourse to the dynamic programming principle. By analyzing the properties of the free boundary problem, we provide an explicit characterization of model parameters for which the value function is finite. Furthermore, we prove that the value function, as well as the slopes of the lines demarcating the no-trading region, can be expanded as a series of integer powers of [lambda superscript 1/3]. The coefficients of arbitrary order in this expansion can be computed. / text

published_or_final_version / Economics and Finance / Master / Master of Philosophy

published_or_final_version / Housing Management / Master / Master of Housing Management

published_or_final_version / Housing Management / Master / Master of Housing Management

published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

In recent years technical trading rules are widely known by more and more people, not only the academics many investors also learn to apply them in financial markets. One approach of constructing technical trading rules is to use technical indicators, such as moving average(MA) and filter rules. These trading rules are widely used possibly because the technical indicators are simple to compute and can be programmed easily. An alternative approach of constructing technical trading rules is to rely on some chart patterns. However, the patterns and signals detected by these rules are often made by the visual inspection through human eyes. As for as I know, there are no universally acceptable methods of constructing the chart patterns. In 2000, Prof. Andrew Lo and his colleagues are the first ones who define five pairs of chart patterns mathematically. They are Head-and-Shoulders(HS) & Inverted Headand- Shoulders(IHS), Broadening tops(BTOP) & bottoms(BBOT), Triangle tops(TTOP) & bottoms(TBOT), Rectangle tops(RTOP) & bottoms( RBOT) and Double tops(DTOP) & bottoms(DBOT). The basic formulation of a chart pattern consists of two steps: detection of (i) extreme points of a price series; and (ii) shape of the pattern. In Lo et al.(2000), the method of kernel smoothing was used to identify the extreme points. It was admitted by Lo et al. (2000) that the optimal bandwidth used in kernel method is not the best choice and the expert judgement is needed in detecting the bandwidth. In addition, their work considered chart pattern detection only but no buy/sell signal detection. It should be noted that it is possible to have a chart pattern formed without a signal detected, but in this case no transaction will be made. In this thesis, I propose a new class of technical trading rules which aims to resolve the above problems. More specifically, each chart pattern is parameterized by a set of parameters which governs the shape of the pattern, the entry and exit signals of trades. Then the optimal set of parameters can be determined by using genetic algorithms (GAs). The advantage of GA is that they can deal with a high-dimensional optimization problems no matter the parameters to be optimized are continuous or discrete. In addition, GA can also be convenient to use in the situation that the fitness function is not differentiable or has a multi-modal surface. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Spatial autocorrelation is commonly found in the Hedonic Pricing model for real estate prices, but little attention has been paid to identify the causes behind. The primary objective of this research is to examine the causes of spatial autocorrelation in housing prices. Observed autocorrelation is often attributable to the omission of important location characteristics in the modelling process. Since it is practically impossible to exhaustively include all location characteristics, some variables may eventually be omitted, leaving spatially autocorrelated residuals in the Hedonic Pricing model. This thesis proposes a new source of spatial autocorrelation: real estate market liquidity. We hypothesize that liquidity affects the geographical boundary within which buyers and sellers search for price information. When the “immediate vicinity” of a property has few transactions, buyers and sellers may have to search for price information from more distant locations. Therefore, low liquidity in the vicinity of a property should strengthen the spatial autocorrelation of real estate prices. A Spatial - Liquidity Hedonic Pricing (SLHP) model is proposed to test the above hypothesis. The SLHP model generalizes traditional spatial autoregressive models by making the spatial process liquidity dependent. When applied to the apartment market in Hong Kong, the model is operationalized by defining “immediate vicinity” as the building where the subject unit locates. Furthermore, the SLHP model recognizes that past transactions may affect current transactions, but not vice versa, so the spatial weight matrix is simply lower triangular. Under this condition, we have shown that the Maximum Likelihood Estimation is equivalent to the Ordinary Least Squares Estimation. This greatly simplifies the estimation procedures and reduces the empirical analysis to a feasible scale. Based on 15 500 transactions of residential units in Taikooshing, Hong Kong from 1992 to 2006, we conclude that while positive spatial autocorrelation is present in housing prices, its magnitude decreases when liquidity, as measured by the past transaction volume in the immediate vicinity of a subject unit, is high. In addition, we found that current prices are spatially correlated with transactions occurred up to the last three months only, reflecting the relatively high information efficiency of Hong Kong’s residential market. All these results are generally robust across a variety of distance, liquidity, and time weight specifications. This study establishes liquidity as a determinant of spatial autocorrelation in real estate prices. This is a new finding contributing to the economic literature on liquidity effects and technical literature on spatial estimation. Our results not only reveal the spatially dependent price formation process in the real estate market, but also have practical applications on the hedonic modelling of real estate prices for mass valuation and index construction. / published_or_final_version / Real Estate and Construction / Doctoral / Doctor of Philosophy

Research conducted in mathematical finance focuses on the quantitative modeling of financial markets. It allows one to solve financial problems by using mathematical methods and provides understanding and prediction of the complicated financial behaviors. In this thesis, efforts are devoted to derive and extend stochastic optimization models in financial economics and establish practical algorithms for representing and solving problems in mathematical finance. An option gives the holder the right, but not the obligation, to buy or sell an underlying asset at a specified strike price on or before a specified date. In this thesis, a valuation model for a perpetual convertible bond is developed when the price dynamics of the underlying share are governed by Markovian regime-switching models. By making use of the relationship between the convertible bond and an American option, the valuation of a perpetual convertible bond can be transformed into an optimal stopping problem. A novel approach is also proposed to discuss an optimal inventory level of a retail product from a real option perspective in this thesis. The expected present value of the net profit from selling the product which is the objective function of the optimal inventory problem can be given by the actuarial value of a real option. Hence, option pricing techniques are adopted to solve the optimal inventory problem in this thesis. The goal of risk management is to eliminate or minimize the level of risk associated with a business operation. In the risk measurement literature, there is relatively little amount of work focusing on the risk measurement and management of interest rate instruments. This thesis concerns about building a risk measurement framework based on some modern risk measures, such as Value-at-Risk (VaR) and Expected Shortfall (ES), for describing and quantifying the risk of interest rate sensitive instruments. From the lessons of the recent financial turmoils, it is understood that maximizing profits is not the only objective that needs to be taken into account. The consideration for risk control is of primal importance. Hence, an optimal submission problem of bid and ask quotes in the presence of risk constraints is studied in this thesis. The optimal submission problem of bid and ask quotes is formulated as a stochastic optimal control problem. Portfolio management is a professional management of various securities and assets in order to match investment objectives and balance risk against performance. Different choices of time series models for asset price may lead to different portfolio management strategies. In this thesis, a discrete-time dynamic programming approach which is flexible enough to deal with the optimal asset allocation problem under a general stochastic dynamical system is explored. It’s also interesting to analyze the implications of the heteroscedastic effect described by a continuous-time stochastic volatility model for evaluating risk of a cash management problem. In this thesis, a continuous-time dynamic programming approach is employed to investigate the cash management problem under stochastic volatility model and constant volatility model respectively. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Disposition effect is one of the most documented trading anomalies studied in financial market. Its presence has been established over time horizons, time periods and market participants. This study will examine such trading behavior in the housing market. Using Mei Foo Sun Chuen estate, one of the largest and most frequent transacted estate in Hong Kong, we show that disposition effect is present in this market. A major difficulty in the statistical analysis is the presence of censored data problem, which is hard to circumvent in linear regression models. So we adopt a survival analysis approach, which can accommodate the issue and fit the data structure. The other difficulty is the possibility of omitted variables in the analysis. Instead of appealing to instrumental variables model approach, which is widely applied in many research studies on individual behavior but is extremely hard to be justified in a whole market case, we make use of partial identification approach to estimate bounds for the estimates rather than just a point estimate. Even though this seems offer us less precise information, it is still informative, especially when the bounds are narrow, and it is much less vulnerable to the validity of instruments. Besides the above techniques, we use bootstrapping method to estimate the standard errors throughout the analysis in order to make valid inference. There are three main results we have established in this study. First, the disposition effect is present in Hong Kong housing market. It shows up in both in pre-1997 and post-1997 periods, which suggest that it is a general phenomenon rather than a short-term trading pattern arising from a major macroeconomic event. Secondly, we show that it is the nominal perspective loss that matters, but not real loss. This confirms the validity of basic setup of both Prospect theory and most previous empirical studies on the disposition effect. Thirdly, the disposition effect is more significant for short term owner of less than 3 years. In fact, the disposition effect is absent or even reverses for those flat owners of more than 6 years. Comparing to the very first study on disposition effect by Shefrin & Statman (1985), our study makes a step forward in understanding trading behavior. We extend it applicability to housing market while their focus is only on financial market even though we are not the first to attempt the extension. We not only show the presence of disposition effect in the housing market, we also show that disposition effect is time dependent. Our results lead further support to disposition effect that its key component, loss, matters only in nominal term, not in real term. Instead of only applying ordinary least squared regression methods, which is widely used in the literature, we apply partial identification approach to tackle the endogeneity issue and apply duration models to deal with censored data and unobserved heterogeneity issues. All this makes our statistical results more robust. / published_or_final_version / Real Estate and Construction / Doctoral / Doctor of Philosophy

Nowadays, the mobility and globalization of firms make it possible for people to choose their favorite working cities worldwide. Thus beyond employment and income, more and more attention has been paid to the comparison of urban quality of life (UQOL). As housing cost usually consists of the largest share of household budget which is thought as a “ticket” to live in a city, housing prices surely have great impact on the relative value of income and UQOL when one makes a relocation decision. With increasing inter-urban migration in China, the inter-urban real estate development becomes popular. In order to plant right crop for right land, the inter-urban differences on the combination of housing prices, income and UQOL should be well studied. In addition, it is found that cities with high UQOL grow faster because they can attract more talents to work in (Glaeser 2001). But with more and more immigration taken place in high amenity cities, housing prices may rise up faster than workers’ wages. When the advantage of UQOL is offset by the increased housing cost, it would reach a dynamic equilibrium which lets immigration terminate or slow down. Even worse, if housing prices rise higher and higher, talents would have to move out. Therefore, it is noticeable to the urban governments that the pattern of inter-urban competitiveness changes dramatically from the traditional solely economic-driven mode to the sustainable attractiveness by the bundles of housing prices, income and UQOL. This research aims at revealing the quantitative relationship among housing prices, income and UQOL which may give inspiration to city dwellers, developers and governments. Firstly following the compensation theory, a customized equilibrium model is developed to calculate the quantitative value of UQOL. Then a new classification method is proposed to Chinese cities based on their bundles of housing prices, income and UQOL. There are 3-high cities, 2-high (2-high-price&income, 2-high-price&UQOL, 2-high-income&UQOL) cities, 1-high (1-high-price, 1-high-income and 1-high-UQOL) cities and 3-low cities. This classification gives a new vision for city dwellers, developers and governments to recognize the substantive differences among cities which are helpful for decision making, strategy deployment and policy making. Rural labor is suggested to choose 1-high-income cities as early as better. College graduates are advised to enter 2-high-income&UQOL cities as soon as possible. The rich and famous group is recommended to enter 3-high cities to enjoy the most mature service. Inter-urban developers need to take different development strategies in different kinds of cities: develop products at popular locations in 3-high cities, create local good reputation with high-quality housing in cities with high housing prices and enter cities with high UQOL as quickly as possible. For urban governments, it’s important to keep improving UQOL in the course of the economic development. Also, they are advised to control the excessive growth of housing prices especially in 3-high cities. / published_or_final_version / Real Estate and Construction / Doctoral / Doctor of Philosophy