Executive stock option exercise with full and partial information on a drift change point

We analyse the optimal exercise of an executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point, an exponentially distributed random time independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the change point, and seek to optimally exercise the option by maximising its discounted payoff under the physical measure. The first agent has full information, and observes the change point. The second agent has partial information and filters the change point from price observations. This scenario is designed to mimic the positions of two employees of varying seniority, a fully informed executive and a partially informed less senior employee, each of whom receives an ESO. The partial information scenario yields a model under the observation filtration $\widehat{\mathbb{F}}$ in which the stock drift becomes a diffusion driven by the innovations process, an $\widehat{\mathbb{F}}$-Brownian motion also driving the stock under $\widehat{\mathbb{F}}$, and the partial information optimal stopping value function has two spatial dimensions. We rigorously characterise the free boundary PDEs for both agents, establish shape and regularity properties of the associated optimal exercise boundaries, and prove the smooth pasting property in both information scenarios, exploiting some stochastic flow ideas to do so in the partial information case. We develop finite difference algorithms to numerically solve both agents' exercise and valuation problems and illustrate that the additional information of the fully informed agent can result in exercise patterns which exploit the information on the change point, lending credence to empirical studies which suggest that privileged information of bad news is a factor leading to early exercise of ESOs prior to poor stock price performance.Comment: 48 pages, final version, accepted for publication in SIAM Journal on Financial Mathematic

A Multidimensional Exponential Utility Indifference Pricing Model with Applications to Counterparty Risk

This paper considers exponential utility indifference pricing for a multidimensional non-traded assets model subject to inter-temporal default risk, and provides a semigroup approximation for the utility indifference price. The key tool is the splitting method, whose convergence is proved based on the Barles-Souganidis monotone scheme, and the convergence rate is derived based on Krylov's shaking the coefficients technique. We apply our methodology to study the counterparty risk of derivatives in incomplete markets.Comment: 29 pages, 5 figure

Partial liquidation under reference-dependent preferences

We propose a multiple optimal stopping model where an investor can sell a divisible asset position at times of her choosing. Investors have S-shaped reference-dependent preferences, whereby utility is defined over gains and losses relative to a reference level and is concave over gains and convex over losses. For a price process following a time-homogeneous diffusion, we employ the constructive potential-theoretic solution method developed by Dayanik and Karatzas (Stoch. Process. Appl. 107:173–212, 2003). As an example, we revisit the single optimal stopping model of Kyle et al. (J. Econ. Theory 129:273–288, 2006) to allow partial liquidation. In contrast to the extant literature, we find that the investor may partially liquidate the asset at distinct price thresholds above the reference level. Under other parameter combinations, the investor sells the asset in a block, either at or above the reference level

Randomized strategies and prospect theory in a dynamic context

When prospect theory (PT) is applied in a dynamic context, the probability weighting com- ponent brings new challenges. We study PT agents facing optimal timing decisions and consider the impact of allowing them to follow randomized strategies. In a continuous-time model of gam- bling and optimal stopping, Ebert and Strack (2015) show that a naive PT investor with access only to pure strategies never stops. We show that allowing randomization can signi cantly alter the predictions of their model, and can result in voluntary cessation of gambling

Cautious Stochastic Choice, optimal stopping and deliberate randomization

We study Cautious Stochastic Choice (CSC) agents facing optimal timing decisions in a dynamic setting. In an expected utility setting, the optimal strategy is always a threshold strategy - to stop/sell the first time the price process exits an interval. In contrast, we show that in the CSC setting, where the agent has a family of utility functions and is concerned with the worst case certainty equivalent, the optimal strategy may be of non-threshold form and may involve randomization. We provide some carefully constructed examples, including one where we can solve explicitly for the optimal stopping rule and show it is a non-trivial mixture of threshold strategies. Our model is consistent with recent experimental evidence in dynamic setups whereby individuals do not play cut-off or threshold strategies

Conditions for successful technology enabled learning

This paper reports on the findings of a 16 month project funded by the Australian Government Office for Learning and Teaching. The project utilized an iterative mixed method design to investigate (a) what digital technologies are used and valued by students and educators for learning, and (b) the different factors within the ‘ecology’ of the university that contribute to these successful uses of digital technology. In total 2838 students and staff across two Australian universities and a further 114 leaders from all 39 Australian universities participated in the project. Through large scale surveys and in-depth case studies thirteen ‘conditions for success’ were identified that appeared to stimulate, support, and/or sustain specific success stories. These conditions relate to different aspects of the ‘ecology’ of higher education – from individual skills and attitudes through to institutional policymaking. This paper describes the conditions for success, and concludes with challenges to the higher education sector

Research students exhibition catalogue 2011

The catalogue demonstrates the scope and vibrancy of current inquiries and pays tribute to the creative capacity and investment of UCA research students. It brings together contributions from students who are at different stages in their research ad/venture. Their explorations are connected by the centrality of contemporary material practices as focal point for the reconsideration of societal values, cultural symbols and rituals and their meaning, and the trans/formation of individual, collective and national identities The media and formats employed range from cloth, jewellery and ceramics to analogue film, the human voice and the representation of dress and fashionin virtual environments. Thematic interests span from explorations at the interface of art and medical science to an investigation of the role of art in contested spaces, or the role of metonymy in ‘how the arts think’ And whilst the projects are motivated by personal curiosity and passion, their outcomes transcend the boundaries of individual practice and offer new insights, under-standing and applications for the benefit of wider society. Prof. Kerstin Me

Organisational and student characteristics, fidelity, funding models, and unit costs of recovery colleges in 28 countries: a cross-sectional survey

Background: Recovery colleges were developed in England to support the recovery of individuals who have mental health symptoms or mental illness. They have been founded in many countries but there has been little international research on recovery colleges and no studies investigating their staffing, fidelity, or costs. We aimed to characterise recovery colleges internationally, to understand organisational and student characteristics, fidelity, and budget. // Methods: In this cross-sectional study, we identified all countries in which recovery colleges exist. We repeated a cross-sectional survey done in England for recovery colleges in 28 countries. In both surveys, recovery colleges were defined as services that supported personal recovery, that were coproduced with students and staff, and where students learned collaboratively with trainers. Recovery college managers completed the survey. The survey included questions about organisational and student characteristics, fidelity to the RECOLLECT Fidelity Measure, funding models, and unit costs. Recovery colleges were grouped by country and continent and presented descriptively. We used regression models to explore continental differences in fidelity, using England as the reference group. // Findings: We identified 221 recovery colleges operating across 28 countries, in five continents. Overall, 174 (79%) of 221 recovery colleges participated. Most recovery colleges scored highly on fidelity. Overall scores for fidelity (β=–2·88, 95% CI 4·44 to –1·32; p=0·0001), coproduction (odds ratio [OR] 0·10, 95% CI 0·03 to 0·33; p<0·0001), and being tailored to the student (OR 0·10, 0·02 to 0·39; p=0·0010), were lower for recovery colleges in Asia than in England. No other significant differences were identified between recovery colleges in England, and those in other continents where recovery colleges were present. 133 recovery colleges provided data on annual budgets, which ranged from €0 to €2 550 000, varying extensively within and between continents. From included data, all annual budgets reported by the college added up to €30 million, providing 19 864 courses for 55 161 students. // Interpretation: Recovery colleges exist in many countries. There is an international consensus on key operating principles, especially equality and a commitment to recovery, and most recovery colleges achieve moderate to high fidelity to the original model, irrespective of the income band of their country. Cultural differences need to be considered in assessing coproduction and approaches to individualising support. // Funding: National Institute for Health and Care Research