Optimal investment with derivative securities

We consider an investor who maximizes expected exponential utility of terminal wealth, combining a static position in derivative securities with a traditional dynamic trading strategy in stocks. Our main result, obtained by studying the strict concavity of the utility-indifference price as a function of the static positions, is that, in a quite general incomplete arbitrage-free market, there exists a unique optimal strategy for the investor.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47871/1/780_2005_Article_154.pd

A note on market completeness with American put options

We consider a non necessarily complete financial market with one bond and one risky asset, whose price process is modelled by a suitably integrable, strictly positive, càdlàg process $S$ over $[0, T]$. Every option price is defined as the conditional expectation under a given equivalent (true) martingale measure $\mathbb P$, the same for all options. We show that every positive contingent claim on $S$ can be approximately replicated (in $L^2$-sense) by investing dynamically in the underlying and statically in all American put options (of every strike price $k$ and with the same maturity $T$). We also provide a counter-example to static hedging with European call options of all strike prices and all maturities $t\leq T$.

Forward Exponential Performances: Pricing and Optimal Risk Sharing

In a Markovian stochastic volatility model, we consider financial agents whose investment criteria are modelled by forward exponential performance processes. The problem of contingent claim indifference valuation is first addressed and a number of properties are proved and discussed. Special attention is given to the comparison between the forward exponential and the backward exponential utility indifference valuation. In addition, we construct the problem of optimal risk sharing in this forward setting and solve it when the agents' forward performance criteria are exponential.Comment: 29 page

Sensitivity analysis of utility-based prices and risk-tolerance wealth processes

In the general framework of a semimartingale financial model and a utility function $U$ defined on the positive real line, we compute the first-order expansion of marginal utility-based prices with respect to a ``small'' number of random endowments. We show that this linear approximation has some important qualitative properties if and only if there is a risk-tolerance wealth process. In particular, they hold true in the following polar cases: \begin{tabular}@p97mm@ for any utility function $U$, if and only if the set of state price densities has a greatest element from the point of view of second-order stochastic dominance;for any financial model, if and only if $U$ is a power utility function ($U$ is an exponential utility function if it is defined on the whole real line). \end{tabular}Comment: Published at http://dx.doi.org/10.1214/105051606000000529 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Accounting for Risk Aversion in Derivatives Purchase Timing

We study the problem of optimal timing to buy/sell derivatives by a risk-averse agent in incomplete markets. Adopting the exponential utility indifference valuation, we investigate this timing flexibility and the associated delayed purchase premium. This leads to a stochastic control and optimal stopping problem that combines the observed market price dynamics and the agent's risk preferences. Our results extend recent work on indifference valuation of American options, as well as the authors' first paper (Leung and Ludkovski, SIAM J. Fin. Math., 2011). In the case of Markovian models of contracts on non-traded assets, we provide analytical characterizations and numerical studies of the optimal purchase strategies, with applications to both equity and credit derivatives

Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility

The final publication is available at Elsevier via http://dx.doi.org/10.1016/j.jedc.2018.01.023 © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/This paper provides a derivative-based optimal investment strategy for an ambiguity-adverse pension investor who faces not only risks from time-varying income and market return volatility but also uncertain economic conditions over a long time horizon. We derive a robust dynamic derivative strategy and show that the optimal strategy under ambiguity aversion reduces the exposures to market return risk and volatility risk and that the investor holds opposite positions for the two risk exposures. In the presence of a derivative, ambiguity has distinct effects on the optimal investment strategy. More important, we demonstrate the utility improvement when considering ambiguity and exploiting derivatives and show that ambiguity aversion and derivative trading significantly improve utility when return volatility increases. This improvement becomes more significant under ambiguity aversion over a long investment horizon.National Natural Science Foundation of China under Grant [71771220, 71721001, 71571195, 11371155, 11326199, 11771158]Major Program of the National Social Science Foundation of China [No. 17ZDA073]Fok Ying Tung Education Foundation for Young Teachers in the Higher Education Institutions of China [No. 151081]Guangdong Natural Science Foundation for Research Team [No. 2014A030312003]Guangdong Natural Science Funds for Distinguished Young Scholars [No. 2015A030306040]Natural Science Foundation of Guangdong Province of China [No. 2014A030310195]Insurance Society of China [No. ISCKT2016-N-l-07