Optimal Investment With Default Risk

In this paper, we investigate how investors who face both equity risk and credit risk would optimally allocate their financial wealth in a dynamic continuous-time setup. We model credit risk through the defaultable zero-coupon bond and solve the dynamics of its price after pricing it. Using stochastic control methods, we obtain a closed-form solution to this investment problem and characterize its variation with respect to different factors in the economy. We find that non-zero recovery rate of the credit-risky bond affects investors' decision in a fundamental way. Because of this, investors try to time the market conditions in their decision making process. It also induces hedging term in this setup of otherwise deterministic investment opportunity set. Through numerical examples, we show that the inclusion of credit market is shown to be able to enhance investors' welfare.Default Risk; Corporate Bond; Asset Allocation; Welfare Analysis

Existence of positive solutions for discrete delta-nabla fractional boundary value problems with p-Laplacian

Abstract In this paper, we consider a discrete delta-nabla boundary value problem for the fractional difference equation with p-Laplacian △ v − 2 β ( φ p ( b ∇ ν x ( t ) ) ) + λ f ( t − ν + β + 1 , x ( t − ν + β + 1 ) , [ b ∇ ε x ( t ) ] t − ν + β + ε + 1 ) = 0 , x ( b ) = 0 , [ b ∇ ν x ( t ) ] ν − 2 = 0 , x ( − 1 ) = ∑ t = 0 b − 1 x ( t ) A ( t ) , $$\begin{aligned}& {\triangle_{v-2}^{\beta}} \bigl({\varphi_{p} \bigl({_{b}\nabla^{\nu }}x(t) \bigr)} \bigr)+{\lambda} {f \bigl(t-\nu+\beta+1,x(t-\nu+\beta +1), \bigl[_{b}\nabla^{\varepsilon}x(t) \bigr]_{t-\nu+\beta+\varepsilon+1} \bigr)}=0, \\& x(b)=0,\quad\quad \bigl[_{b}\nabla^{\nu}x(t) \bigr]_{\nu-2}=0,\quad\quad x(-1)=\sum_{t=0}^{b-1}{x(t)A(t)}, \end{aligned}$$ where t ∈ T = [ ν − β − 1 , b + ν − β − 1 ] N ν − β − 1 $t\in\mathbb{T}=[\nu-\beta-1,b+\nu-\beta-1]_{\mathbb{N}_{\nu-\beta-1}}$ . △ ν − 2 β ${\triangle_{\nu-2}^{\beta}}$ , ∇ ν b ${_{b}\nabla^{\nu}}$ are left and right fractional difference operators, respectively, and φ p ( s ) = | s | p − 2 s $\varphi_{p}(s)=|s|^{p-2}s$ , p > 1 $p>1$ . By using the method of upper and lower solution and the Schauder fixed point theorem, we obtain the existence of positive solutions for the above boundary value problem; and applying a monotone iterative technique, we establish iterative schemes for approximating the solution

Multiple Solutions for a Fractional Difference Boundary Value Problem via Variational Approach

By establishing the corresponding variational framework and using the mountain pass theorem, linking theorem, and Clark theorem in critical point theory, we give the existence of multiple solutions for a fractional difference boundary value problem with parameter. Under some suitable assumptions, we obtain some results which ensure the existence of a well precise interval of parameter for which the problem admits multiple solutions. Some examples are presented to illustrate the main results

Making the unconventional mu(2)-P bridging binding mode more conventional in phosphinine complexes

Phosphinines, as aromatic heterocycles, usually engage in coordination as η1-P σ-complexes or η6-phosphinine π-complexes. The μ2-P bridging coordination mode is rarely observed. With the aim to study the effect of different electronic configurations of phosphinines on the coordination modes, a series of anionic phosphinin-2-olates and neutral phosphinin-2-ols were prepared with moderate to high yield. Then the coordination chemistry of these two series was studied in detail towards coinage metals (Au(I) and Cu(I)). It is observed that the anionic phosphinin-2-olates possess a higher tendency to take a bridging position between two metal centers compared to the neutral phosphinin-2-ols. Based on these experimental findings bolstered by DFT calculations, some insight is gained on how the unconventional μ2-P phosphinine bridging coordination mode can be made more conventional and used for the synthesis of polynuclear complexes.ISSN:2041-6520ISSN:2041-653