Forest encroachment into savanna is occurring at an unprecedented rate across tropical Africa, leading to a loss of valuable savanna habitat. One of the first stages of forest encroachment is the establishment of tree seedlings at the forest-savanna transition. This study examines the demographic bottleneck in the seedlings of five species of tropical forest pioneer trees in a forest-savanna transition zone in West Africa. Five species of tropical pioneer forest tree seedlings were planted in savanna, mixed/transition, and forest vegetation types and grown for 12 months, during which time fire occurred in the area. We examined seedling survival rates, height, and stem diameter before and after fire; and seedling biomass and starch allocation patterns after fire. Seedling survival rates were significantly affected by fire, drought, and vegetation type. Seedlings that preferentially allocated more resources to increasing root and leaf starch (starch storage helps recovery from fire) survived better in savanna environments (frequently burnt), while seedlings that allocated more resources to growth and resource-capture traits (height, the number of leaves, stem diameter, specific leaf area, specific root length, root-to-shoot ratio) survived better in mixed/transition and forest environments. Larger (taller with a greater stem diameter) seedlings survived burning better than smaller seedlings. However, larger seedlings survived better than smaller ones even in the absence of fire. Bombax buonopozense was the forest species that survived best in the savanna environment, likely as a result of increased access to light allowing greater investment in belowground starch storage capacity and therefore a greater ability to cope with fire. Synthesis: Forest pioneer tree species survived best through fire and drought in the savanna compared to the other two vegetation types. This was likely a result of the open-canopied savanna providing greater access to light, thereby releasing seedlings from light limitation and enabling them to make and store more starch. Fire can be used as a management tool for controlling forest encroachment into savanna as it significantly affects seedling survival. However, if rainfall increases as a result of global change factors, encroachment may be more difficult to control as seedling survival ostensibly increases when the pressure of drought is lifted. We propose B. buonopozense as an indicator species for forest encroachment into savanna in West African forest-savanna transitions.

Winners and losers

We give a survey of the developments in the theory of Backward Stochastic Differential Equations during the last 20 years, including the solutions’ existence and uniqueness, comparison theorem, nonlinear Feynman-Kac formula, g-expectation and many other important results in BSDE theory and their applications to dynamic pricing and hedging in an incomplete financial market. We also present our new framework of nonlinear expectation and its applications to financial risk measures under uncertainty of probability distributions. The generalized form of law of large numbers and central limit theorem under sublinear expectation shows that the limit distribution is a sublinear Gnormal distribution. A new type of Brownian motion, G-Brownian motion, is constructed which is a continuous stochastic process with independent and stationary increments under a sublinear expectation (or a nonlinear expectation).

Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications

We derive a closed form portfolio optimization rule for an investor who is diffident about mean return and volatility estimates, and has a CRRA utility. Confidence is here represented using ellipsoidal uncertainty sets for the drift, given a (compact valued) volatility realization. This specification affords a simple and concise analysis, as the agent becomes observationally equivalent to one with constant, worst case parameters. The result is based on a max–min Hamilton–Jacobi–Bellman–Isaacs PDE, which extends the classical Merton problem and reverts to it for an ambiguity-neutral investor.

/pdf/the-robust-merton-problem-of-an-ambiguity-averse-investor-11rp3vuwsx.pdf

The robust Merton problem of an ambiguity averse investor

In this paper, we study the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion (GSDEs) with integral-Lipschitz coefficients.

On the existence and uniqueness of solutions to stochastic differential equations driven by G -Brownian motion with integral-Lipschitz coefficients

We study a robust portfolio optimization problem under model uncertainty for an investor with logarithmic or power utility. The uncertainty is specified by a set of possible Levy triplets; that is, possible instantaneous drift, volatility and jump characteristics of the price process. We show that an optimal investment strategy exists and compute it in semi-closed form. Moreover, we provide a saddle point analysis describing a worst-case model.

/pdf/robust-utility-maximization-with-levy-processes-5aehb06r20.pdf

Robust utility maximization with lévy processes

We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of non-equivalent multiple priors. We solve the problem completely by identifying the worst-case measure. Our setup also allows to consider interest rate uncertainty; we show that under some robust parameter constellations, the investor optimally puts all his wealth into the asset market, and does not save or borrow at all.

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID2379537_code1809478.pdf?abstractid=2377452&mirid=1

Optimal Consumption and Portfolio Choice with Ambiguity

In this paper, we study the property of continuous dependence on the parameters of stochastic integrals and solutions of stochastic differential equations driven by the G-Brownian motion. In addition, the uniqueness and comparison theorems for those stochastic differential equations with non-Lipschitz coefficients are obtained.

Some properties of stochastic differential equations driven by the G-Brownian motion

We consider optimal consumption and portfolio choice in the presence of Knightian uncertainty in continuous-time. We embed the problem into the new framework of stochastic calculus for such settings, dealing in particular with the issue of non-equivalent multiple priors.
We solve the problem completely by identifying the worst-case measure. Our setup also allows to consider interest rate uncertainty; we show that under some robust parameter constellations, the investor optimally puts all his wealth into the asset market, and does not save or borrow at all.

Qian Lin

Papers

Optimal Consumption and Portfolio Choice with Ambiguity

Some properties of stochastic differential equations driven by the G-Brownian motion

Optimal consumption and portfolio choice with ambiguity

Local time and Tanaka formula for the G-Brownian motion

A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals